RECENT research on structured mesh flow solver for aerodynamic problems shows that for practical levels of
|
|
- Winifred Perry
- 6 years ago
- Views:
Transcription
1 A Hgh-Order Accurate Unstructured GMRES Algorthm for Invscd Compressble Flows A. ejat * and C. Ollver-Gooch Department of Mechancal Engneerng, The Unversty of Brtsh Columba, Appled Scence Lane, Vancouver, BC V6T Z4, Canada A precondtoned matrx-free GMRES method s presented for unstructured hgherorder computaton of D nvscd compressble flows. Lower-Upper Symmetrc Gauss-Sedel (LU-SGS has been used as the precondtonng strategy, and an approxmate frst order Jacoban as the precondtonng matrx. The numercal algorthm demonstrates promsng convergence performance for both the second and the thrd order dscretzaton methods n supersonc flow. I. Introducton RECET research on structured mesh flow solver for aerodynamc problems shows that for practcal levels of accuracy usng a hgher order accurate method can reduce computaton tme and memory usage and mprove qualty of the soluton compared to a second-order scheme., To take advantage of the hgh flexblty n mesh generaton and adaptaton for unstructured meshes, we want to apply hgher-order accurate methods for unstructured meshes. Ths approach combnes benefts of hgher-order methods and unstructured meshes. Although hgh-order accurate methods for unstructured meshes are reasonably well establshed, -6 applcaton of these methods for physcally complcated flows s stll a challenge due to very slow convergence. Ths elmnates the effcency benefts of hgher-order unstructured dscretzaton and lmts ther applcaton for practcal purposes. Consequently, convergence acceleraton becomes the key ssue for the practcal usage of hgher-order unstructured solvers. ewton-gmres famly solvers 7- are a commonly used method due to ther property of fast convergence. Snce GMRES algorthm only needs matrx vector products and theses products can be computed by matrx free approach, matrx-free GMRES 9 s a very attractve technque for dealng wth the complcated Jacoban matrces. Ths approach saves memory usage consderably and, removes the problem of explct formng of the Jacoban matrx. Recent results of an unstructured mesh solver for Posson's equaton clearly showed the possblty of reducng computatonal cost requred for a gven level of soluton accuracy usng hgher-order methods and matrx free GMRES as a convergence acceleraton technque. As Posson's equaton s smple and has a lnear flux, the resultant Jacoban matrx s well-condtoned, and the convergence rate for GMRES technque s good. In case of more complex problems, ncludng CFD problems, the Jacoban s typcally ll-condtoned and effectve precondtonng s necessary for good GMRES convergence. Several authors have studed the effect of varous precondtong methods on convergence of matrx-free GMRES both for structured and unstructured meshes. 7-9,,,4 Ther research shows ncomplete lower-upper (ILU factorzaton of the approxmate Jacoban s a very effcent precondtonng strategy for CFD problems. Delanaye et al. 5 presented an ILU precondtoned matrx-free GMRES solver for Euler and aver-stokes equatons on unstructured adaptve grds usng quadratc reconstructon. A totally matrx-free mplct method was ntroduced by Luo et al. 6 for D compressble flows usng GMRES-LUSGS (Lower-Upper Symmetrc Gauss-Sedel. They completely elmnated the storage of the precondtonng Jacoban matrx by approxmatng the Jacoban wth numercal fluxes. Our objectve n ths research s to develop an effcent and accurate unstructured solver for nvscd compressble flud flows. Ths paper presents prelmnary results of usng Lower-Upper Symmetrc Gauss-Sedel (LU-SGS for precondtonng of the matrx-free GMRES to compute the hgher-order soluton of Euler equatons. * PhD Canddate, nejat@mech.ubc.ca, Student Member AIAA. Assocate Professor, cfog@mech.ubc.ca, Member AIAA. Amercan Insttute of Aeronautcs and Astronautcs
2 II. Governng Equatons The unsteady (D Euler equatons whch model compressble nvscd flud flows, are conservaton equatons for mass, momentum, and energy. The fnte-volume formulaton of Euler equatons for an arbtrary control volume can be wrtten n the followng form of a volume and a surface ntegral: d dt cv Udv + FdA = 0 cs ( where U ρ ρu = ρv E, F ρun ρuun + Pnˆ = ρvun + Pnˆ ρ( E + P u x y n ( T In (, u = u nˆ + vnˆ and ( ρ ρu ρv E are the denstes of mass, x-momentum, y-momentum, and n x y energy, respectvely. The energy s related to the pressure by the perfect gas equaton of state: E = P /( γ + ρ(u + v /, wthγ the rato of specfc heats for the gas. III. Algorthm Descrpton The ntegral form of Eq. ( (for control volume can be wrtten n the form of Eq. (- where R (.e. resdual of the governng equatons represents the spatal dscretzaton operator. Lnearzaton n tme and applyng mplct tme ntegraton leads to mplct tme advance formula (Eq. (-: du dt + R = 0 (- I R n+ n ( + δu = R t, δ U = U U (- R where n Eq. (- s the Jacoban matrx resultng from the resdual lnearzaton. Eq. (- s a large lnear system of equatons whch should be solved at each tme step to obtan an update for the vector of unknowns. As we are only nterested n steady state soluton, the tme marchng process contnues tll the resdual of the lnear system practcally converges to zero. A. Spatal Dscretzaton For spatal dscretzaton, a hgher-order accurate least-square reconstructon scheme 6 has been used n the nteror of the doman to compute flow quanttes at flux ntegraton ponts to the desred accuracy. Fluxes at control volume boundares are calculated by Roe s flux dfference-splttng formula 7 usng reconstructed flow quanttes. Havng computed the fluxes, we use Gauss quadrature to ntegrate the fluxes to the same order of accuracy as the reconstructon. Hgh-order accurate boundary condtons are also used. 6 B. Lnear System Solver Drect methods for solvng the large lnear system of Eq.(- resultng from the dscretzaton of governng equatons at each tme step are not computatonally tractable. Therefore teratve technques such as Krylov famly methods are beng used for that purpose. 9 The lnear system s asymmetrc both n fll and values makng GMRES 8 Amercan Insttute of Aeronautcs and Astronautcs
3 the obvous frst choce among teratve solvers. The lnear system arsng from a hgh-order dscretzaton has four to fve tmes as many non-zero entres as a second-order scheme. Because of the sze of these matrces and the dffculty n computng ther entres analytcally (even for the second order, we use a matrx-free mplementaton of GMRES 9. In the case of Euler equatons wth nonlnear flux functon and possble dscontnutes n the soluton, usng a hgh-order dscretzaton makes the Jacoban matrx even more off-dagonally domnant and qute llcondtoned. Ths degrades or stalls the convergence of GMRES, whch s hghly dependent on the condton number of the Jacoban matrx. Therefore usng a precondtoner for GMRES becomes necessary for practcal purposes. C. Precondtoned GMRES As prevously mentoned, n order to enhance the convergence performance of GMRES solver for complcated lnear systems, t s necessary to apply precondtonng. In prncpal precondtonng s to solve a modfed lnear system whch s relatvely better condtoned than the orgnal system. Equaton (4 shows the modfed system usng rght-precondtonng. AM ( MX = b (4 M n (4 s an approxmaton to matrx A whch has smpler structure and better condton number and consequently s easer to nvert. If M s a good approxmaton to A, AM becomes close to dentty matrx, ncreasng the 9 performance of the lnear solver. We have chosen to use a matrx-free mplementaton of flexble GMRES (FGMRES. FGMRES satsfes the resdual norm mnmzaton property over the precondtoned Krylov subspace lke standard GMRES, but allows varaton n the precondtoner! As a precondtoner, we use LU-SGS, an teratve lnear solver that has recently receved a far amount of attenton both as a precondtoner and as a solver 6,0, and has been shown to be more effcent than ILU n some cases. 6,9 D. Jacoban Matrx Approxmaton Unlke the orgnal lnear system matrx A, the precondtoner matrx, M, must be bult explctly. We compute an approxmate form of the frst-order Jacoban matrx, reducng the sze and complexty of the precondtoner matrx M. To buld the Jacoban (precondtoner matrx we frst defne the resdual for a typcal cell n terms of flux functons at the control volume faces. For the cell wth the drect neghbors of, and (Fg., the Fgure. A typcal control volume wth ts frst neghbors resdual can be recast n the form of Eq. (5, where length. nˆ s an outward normal vector for each face and l s the face R = + (5 F nˆ ds = F(U,U ( nˆ l + F(U,U ( nˆl F(U,U ( nˆ l faces,,, Amercan Insttute of Aeronautcs and Astronautcs
4 The next step s takng dervatve of the resdual functon respect to the soluton vector of U at control volume and ts neghbors. Eq. (6- through Eq. (6-4 represent the row entres of the Jacoban matrx. Here, we only consder the frst neghbors as the Jacoban matrx s beng computed to the frst order of accuracy. J(, R = = ( nˆl F(U,U, (6- J(, R F(U = = ( nˆ l, (6-,U J(, R F(U,U = = ( nˆ l, (6- J(, R = F(U =,U F(U,U F(U,U ( nˆl, + ( nˆ l, + U ( nˆl, (6-4 The fluxes at control volume faces are calculated based on Roe s flux formula; 7 for example, for the face between cell and ts neghbor, cell, the flux functon can be expressed by Eq. (7. F(U,U = ( F(U + F(U A ~ (U (, U (7 Therefore the flux functon dervatve terms n Eq. (6- through Eq. (6-4 smply can be computed by gnorng changes n A ~ matrx. Equaton (8- and Eq. (8- show examples of such dervatves. F(U,U = ( F ( A ~ (, (8- F(U,U F = ( ( + U (, A ~ (8- E. Start up process and ewton-gmres teraton As convergence performance and stablty of the ewton-gmres technque, especally for compressble flows, are qute senstve to the start up, we have to do several mplct teratons before swtchng to ewton-gmres teraton. Equaton (- s used for mplct pre-teratons. For the Left hand sde we use the approxmate frst order Jacoban, whle the resduals n the rght hand sde are beng computed to the rght order of accuracy. The LU-SGS algorthm s used as a lner solver for these pre-teratons. Then we swtch to ewton-gmres teraton; at ths stage I the term n Eq. (- s removed (.e. takng nfnte tme step. GMRES s used to solve the resultant lnear t system at each ewton teraton. However completely solvng the lnear system at each ewton teraton does not necessarly accelerate overall convergence. Because of the non-lnearty of the equatons, ewton teraton would not accurately represent the soluton and solvng the system completely would result n excessve but not helpful computatons. Wasted computaton can be reduced by usng Inexact-ewton method,. Multple GMRES nner teratons at each ewton outer teraton are appled to decrease the resdual of the lnear system by some factor 4 Amercan Insttute of Aeronautcs and Astronautcs
5 usng restart. Our experence (at least wth the presented test cases shows that normally GMRES teraton wthout restart would provde us enough drop n resdual of the lnear system. Therefore we perform one GMRES teraton per ewton teraton. Wth ths approach we do not acheve the quadratc convergence rate of ewton method but we do reach convergence n less CPU-Tme. IV. Results To nvestgate the convergence performance and robustness of the purposed GMRES solver wth a hgher order unstructured dscretzaton, dfferent supersonc flow cases have been studed. Here for brevty, we present two of them whch show the general convergence behavor of our numercal experments. The frst test case (Fg. s a supersonc duct wth a.5 (deg ramp. The ramp starts at x=0.04m and ends at x=0.m. The total length of the duct s.m and has a heght of 0.m at the nlet secton. The nflow Mach number s equal to. We have used a coarse mesh of 578 control volumes for ths case wth some refnement at the ramp s start and end ponts to capture the shock and expanson waves properly at those locatons. The second test case s a Damond arfol (5% thckness wth 77 control volumes. We use 80 control volumes along the chord wth the proper refnement at leadng and tralng edges and also apex of the arfol (Fg.. The far feld Mach number s agan and the angle of attack s zero. For both cases, 00 mplct pre-teratons have been performed wth the startng CFL=.0 whch ncreases gradually to 00, and a fxed Krylov-subspace sze of 40 s used. F. Supersonc duct The resdual convergence hstory both n terms of CPU-Tme and resdual evaluatons has been shown n Fg. 4 and Fg. 5. GMRES-LUSGS decreases the resdual by 0 order of magntude n 6 teratons for nd order and 7 teratons for rd order. For both orders of accuracy, L-norm of the resdual s reduced by 0 orders of magntude n 000 resdual evaluatons. However as each resdual evaluaton for the rd order dscretzaton s more expensve than for nd order, the rd order CPU-tme s larger. Table shows the summary of the convergence performance for ths case. Table. Convergence summary for supersonc duct nd order rd order CPU-Tme (Sec Resdual Evaluatons GMRES Iteratons. 6 7 G. Damond arfol Supersonc flow feld around the damond arfol has been computed, usng second and thrd order dscretzaton. The convergence summary s shown n Table.. Ths s the case that actually usng hgher-order dscretzaton has mproved the overall performance of the computaton, and both CPU-Tme and number of resdual evaluatons for the rd order dscretzaton are less than these quanttes for the nd order dscretzaton. Fgure 6 and Fg. 7 demonstrate resdual convergence hstory n terms of CPU-Tme and resdual evaluatons respectvely. Steeper slope for the rd order scheme n Fg. 7 means the lnear system arsng from the rd order dscretzaton at each GMRES (ewton teraton s a better representatve for the orgnal non-lnear system. Fgure 8 shows convergence hstory n terms of teraton number. The frst 00 teratons are mplct pre-teratons, takng just small porton of CPU-Tme (Fg. 6. They do not decrease the resduals, but they are necessary for the start up. Fgure. 9 compares computed and the exact pressure coeffcent over the surface along the chord of the arfol. Except the overshoot (at the leadng edge and undershoot (at the apex, agreement wth the exact soluton s reasonably good. It s expected by addng lmter to the present scheme these over and under shoots would be cured consderably. Fgure 0 and Fg. dsplay Mach contours of the flow fled for the nd and rd order dscretzatons. The captured shock waves at leadng and tralng edges and the expanson fan at the apex of the arfol are clearly vsble. The qualty of the 5 Amercan Insttute of Aeronautcs and Astronautcs
6 captured dscontnutes and hgh gradent regons n the flow feld s notceably better for the rd order dscretzaton respect to the nd order case. Table. Convergence summary for damond arfol nd order rd order CPU-Tme (Sec 9 70 Resdual Evaluatons GMRES Iteratons 46 6 V. Concluson A precondtoned matrx-free LUSGS-GMRES algorthm has been presented for hgher-order computaton of soluton of D Euler equatons. The results show that LUSGS-GMRES works almost as effcently for the thrd order dscretzaton as for the second order one. In fact t showed that n some cases, convergence rate can be ncreased usng hgher-order dscretzaton. We are currently workng on extenson of the proposed approach for the 4 th order dscretzaton, followed by a detaled study of soluton accuracy and resource requrements for all orders of accuracy. Acknowledgements Ths research was supported by the Canadan atural Scence and Engneerng Research Councl under Grant OPG References De Rango, S., and Zngg D. W., Aerodynamc Computatons Usng a Hgher-Order Algorthm, AIAA Conference Paper , 999. Zngg, D. W., De Rango, S., emec, M., and Pullam, T. H., Comparson of Several Spatal Dscretzatons for the aver- Stokes Equatons, Journal of Computatonal Physcs, Vol.60, 000, pp Barth, T. J., Fredrckson P. O., and Stuke M., Hgher-Order Soluton of the Euler Equatons on Unstructured Grds Usng Quadratc Reconstructon, AIAA Conference Paper 90-00, Barth, T. J., Recent Development n Hgh-Order K-Exact Reconstructon on Unstructured Meshes, AIAA Conference Paper , Delanaye, M., and Essers, J. A., An Accurate Fnte Volume Scheme for Euler and aver-stokes Equatons on Unstructured Adaptve Grds, AIAA Conference Paper, 95-70, Ollver-Gooch, C., and Van Altena M., A Hgher-Order Accurate Unstructured Mesh Fnte-Volume Scheme for the Advecton-Dffuson Equaton, Journal of Computatonal Physcs, Vol. 8, 00, pp Venkatakrshnan, V., and Mavrpls, D., Implct Solvers for Unstructured Meshes, AIAA Conference Paper 9-57, Orkws, P. D., Comparson of ewton s and Quas-ewton s Method Solvers for aver-stokes Equatons, AIAA Journal, Vol., 99, pp Barth, T. J., and Lnton, S., W., An Unstructured Mesh ewton Solver for Compressble Flud Flow and Its Parallel Implementaton, AIAA Conference Paper 95-0, Ollver-Gooch, C., Toward Problem-Independent Multgrd Convergence Rates for Unstructured Mesh Methods, In 6 th Internatonal Symposum on Computatonal Flud Dynamcs, 995. Pueyo, A., and Zngg, D. W., Improvement to a ewton-krylov Solver for Aerodynamc Flows, AIAA Conference Paper , 998. ejat, A., and Ollver-Gooch C., A Hgh-Order Accurate Unstructured GMRES Solver for Posson's Equaton, CFD 00 Conference Proceedng, 00, pp Blanco, M., and Zngg, D. W., A Fast Solver for the Euler Equatons on Unstructured Grds Usng a ewton-gmres Method, AIAA Conference Paper 97-0, Manzano, L. M., Lassalne, J. V., Wong, P., and Zngg D. W., A ewton-krylov Algorthm for the Euler Equatons Usng Unstructured Grds, AIAA Conference Paper , Delanaye, M., Geuzane, Ph., Essers J. A., and Rogest, P., A Second-Order Fnte-Volume Scheme Solvng Euler and aver-stokes Equatons on Unstructured Adaptve Grds wth an Implct Acceleraton Procedure, AGARD 77 th Flud 6 Amercan Insttute of Aeronautcs and Astronautcs
7 Dynamcs panel Symposum on Progress and Challenges n Computatonal Flud Dynamc Methods and Algorthms, Sevlle, Span, Luo, H., Baum, J. D., and Lohner, R., A Fast Matrx-free mplct Method for compressble Flows on Unstructured Grds, Journal of Computatonal Physcs, Vol 46, 998, pp Roe, P. L., Approxmate Remann Solvers, Parameter vectors, and dfference schemes, Journal of Computatonal Physcs, Vol. 4, 98, pp Saad, Y., and Schultz M. H., A Generalzed Mnmal Resdual Algorthm for Solvng on-symmetrc Lnear Systems, SIAM J. Sc., Stat. Comp. Vol. 7, 986, pp Saad, Y., A Flexble Inner-Outer Precondtoned GMRES Algorthm, SIAM J. Sc.,Stat. Comp. Vol. 4, 99, pp Chen, R. F., and Wang Z. J., Fast, Block Lower-Upper Symmetrc Gauss-Sedel Scheme for Arbtrary Grds, AIAA Journal, Vol. 8, 000, pp Amercan Insttute of Aeronautcs and Astronautcs
8 Fgure. Doman and mesh for the supersonc duct. Fgure. Mesh around the 5% damond arfol. 8 Amercan Insttute of Aeronautcs and Astronautcs
9 Fgure 4. Convergence hstory n terms of CPU-Tme, supersonc duct. Fgure 5. Convergence hstory n terms of Resdual evaluatons, supersonc duct. 9 Amercan Insttute of Aeronautcs and Astronautcs
10 Fgure 6. Convergence hstory n terms of CPU-Tme, damond arfol. Fgure 7. Convergence hstory n terms of Resdual evaluatons, damond arfol. 0 Amercan Insttute of Aeronautcs and Astronautcs
11 Fgure 8. Convergence hstory n terms of teraton number, damond arfol. Fgure 9. Pressure coeffcent along the chord, damond arfol. Amercan Insttute of Aeronautcs and Astronautcs
12 Fgure 0. Mach contours, nd order dscretzaton, damond arfol. Fgure. Mach contours, rd order dscretzaton, damond arfol. Amercan Insttute of Aeronautcs and Astronautcs
Very simple computational domains can be discretized using boundary-fitted structured meshes (also called grids)
Structured meshes Very smple computatonal domans can be dscretzed usng boundary-ftted structured meshes (also called grds) The grd lnes of a Cartesan mesh are parallel to one another Structured meshes
More informationAn inverse problem solution for post-processing of PIV data
An nverse problem soluton for post-processng of PIV data Wt Strycznewcz 1,* 1 Appled Aerodynamcs Laboratory, Insttute of Avaton, Warsaw, Poland *correspondng author: wt.strycznewcz@lot.edu.pl Abstract
More informationAn Accurate Evaluation of Integrals in Convex and Non convex Polygonal Domain by Twelve Node Quadrilateral Finite Element Method
Internatonal Journal of Computatonal and Appled Mathematcs. ISSN 89-4966 Volume, Number (07), pp. 33-4 Research Inda Publcatons http://www.rpublcaton.com An Accurate Evaluaton of Integrals n Convex and
More informationParallel Numerics. 1 Preconditioning & Iterative Solvers (From 2016)
Technsche Unverstät München WSe 6/7 Insttut für Informatk Prof. Dr. Thomas Huckle Dpl.-Math. Benjamn Uekermann Parallel Numercs Exercse : Prevous Exam Questons Precondtonng & Iteratve Solvers (From 6)
More informationPreconditioning Parallel Sparse Iterative Solvers for Circuit Simulation
Precondtonng Parallel Sparse Iteratve Solvers for Crcut Smulaton A. Basermann, U. Jaekel, and K. Hachya 1 Introducton One mportant mathematcal problem n smulaton of large electrcal crcuts s the soluton
More informationImprovement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration
Improvement of Spatal Resoluton Usng BlockMatchng Based Moton Estmaton and Frame Integraton Danya Suga and Takayuk Hamamoto Graduate School of Engneerng, Tokyo Unversty of Scence, 6-3-1, Nuku, Katsuska-ku,
More informationAn Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices
Internatonal Mathematcal Forum, Vol 7, 2012, no 52, 2549-2554 An Applcaton of the Dulmage-Mendelsohn Decomposton to Sparse Null Space Bases of Full Row Rank Matrces Mostafa Khorramzadeh Department of Mathematcal
More informationIMPLEMENTATION OF UNSTRUCTURED GRID GMRES+LU-SGS METHOD ON SHARED-MEMORY, CACHE-BASED PARALLEL COMPUTERS
AIAA-97 IMPLEMENTATION OF UNSTRUCTURED GRID GMRES+LU-SGS METHOD ON SHARED-MEMORY, CACHE-BASED PARALLEL COMPUTERS Dmtr Sharov, Hong Luo, Joseph D. Baum Scence Applcatons Internatonal Corporaton 7 Goodrdge
More informationS1 Note. Basis functions.
S1 Note. Bass functons. Contents Types of bass functons...1 The Fourer bass...2 B-splne bass...3 Power and type I error rates wth dfferent numbers of bass functons...4 Table S1. Smulaton results of type
More informationMathematics 256 a course in differential equations for engineering students
Mathematcs 56 a course n dfferental equatons for engneerng students Chapter 5. More effcent methods of numercal soluton Euler s method s qute neffcent. Because the error s essentally proportonal to the
More informationA HIGH-ORDER SPECTRAL (FINITE) VOLUME METHOD FOR CONSERVATION LAWS ON UNSTRUCTURED GRIDS
AIAA-00-058 A HIGH-ORDER SPECTRAL (FIITE) VOLUME METHOD FOR COSERVATIO LAWS O USTRUCTURED GRIDS Z.J. Wang Department of Mechancal Engneerng Mchgan State Unversty, East Lansng, MI 88 Yen Lu * MS T7B-, ASA
More informationHermite Splines in Lie Groups as Products of Geodesics
Hermte Splnes n Le Groups as Products of Geodescs Ethan Eade Updated May 28, 2017 1 Introducton 1.1 Goal Ths document defnes a curve n the Le group G parametrzed by tme and by structural parameters n the
More informationA MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS
Proceedngs of the Wnter Smulaton Conference M E Kuhl, N M Steger, F B Armstrong, and J A Jones, eds A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Mark W Brantley Chun-Hung
More informationA gradient smoothing method (GSM) for fluid dynamics problems
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluds 2008; 58:1101 1133 Publshed onlne 27 March 2008 n Wley InterScence (www.nterscence.wley.com)..1788 A gradent smoothng method
More informationAn Optimal Algorithm for Prufer Codes *
J. Software Engneerng & Applcatons, 2009, 2: 111-115 do:10.4236/jsea.2009.22016 Publshed Onlne July 2009 (www.scrp.org/journal/jsea) An Optmal Algorthm for Prufer Codes * Xaodong Wang 1, 2, Le Wang 3,
More informationS.P.H. : A SOLUTION TO AVOID USING EROSION CRITERION?
S.P.H. : A SOLUTION TO AVOID USING EROSION CRITERION? Célne GALLET ENSICA 1 place Emle Bloun 31056 TOULOUSE CEDEX e-mal :cgallet@ensca.fr Jean Luc LACOME DYNALIS Immeuble AEROPOLE - Bat 1 5, Avenue Albert
More informationa tree-dmensonal settng. In te presented approac, we construct te ne mes by renng an exstng coarse mes and updatng te nodes of te ne mes accordng to t
Parallel Two-Level Metods for Tree-Dmensonal Transonc Compressble Flow Smulatons on Unstructured Meses R. Atbayev a, X.-C. Ca a, and M. Parascvou b a Department of Computer Scence, Unversty of Colorado,
More informationPHANTOM VORTICITY IN EULER SOLUTIONS ON HIGHLY STRETCHED GRIDS
ICAS 000 CONGRESS PHANTOM VORTICITY IN EULER SOLUTIONS ON HIGHLY STRETCHED GRIDS S. A. Prnce, D. K. Ludlow, N. Qn Cranfeld College of Aeronautcs, Bedfordshre, UK Currently DERA Bedford, UK Keywords: Phantom
More informationarxiv: v3 [cs.na] 18 Mar 2015
A Fast Block Low-Rank Dense Solver wth Applcatons to Fnte-Element Matrces AmrHossen Amnfar a,1,, Svaram Ambkasaran b,, Erc Darve c,1 a 496 Lomta Mall, Room 14, Stanford, CA, 9435 b Warren Weaver Hall,
More information2x x l. Module 3: Element Properties Lecture 4: Lagrange and Serendipity Elements
Module 3: Element Propertes Lecture : Lagrange and Serendpty Elements 5 In last lecture note, the nterpolaton functons are derved on the bass of assumed polynomal from Pascal s trangle for the fled varable.
More informationSolving two-person zero-sum game by Matlab
Appled Mechancs and Materals Onlne: 2011-02-02 ISSN: 1662-7482, Vols. 50-51, pp 262-265 do:10.4028/www.scentfc.net/amm.50-51.262 2011 Trans Tech Publcatons, Swtzerland Solvng two-person zero-sum game by
More informationAMath 483/583 Lecture 21 May 13, Notes: Notes: Jacobi iteration. Notes: Jacobi with OpenMP coarse grain
AMath 483/583 Lecture 21 May 13, 2011 Today: OpenMP and MPI versons of Jacob teraton Gauss-Sedel and SOR teratve methods Next week: More MPI Debuggng and totalvew GPU computng Read: Class notes and references
More informationChapter 6 Programmng the fnte element method Inow turn to the man subject of ths book: The mplementaton of the fnte element algorthm n computer programs. In order to make my dscusson as straghtforward
More informationStructural Optimization Using OPTIMIZER Program
SprngerLnk - Book Chapter http://www.sprngerlnk.com/content/m28478j4372qh274/?prnt=true ق.ظ 1 of 2 2009/03/12 11:30 Book Chapter large verson Structural Optmzaton Usng OPTIMIZER Program Book III European
More informationDifferential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations
Graduate Theses and Dssertatons Graduate College 2011 Dfferental formulaton of dscontnuous Galerkn and related methods for compressble Euler and Naver-Stokes equatons Hayang Gao Iowa State Unversty Follow
More informationJournal of Computational Physics
Journal of Computatonal Physcs 230 (2011) 2540 2561 Contents lsts avalable at ScenceDrect Journal of Computatonal Physcs journal homepage: www.elsever.com/locate/jcp A grd based partcle method for solvng
More informationNORMALE. A modied structured central scheme for. 2D hyperbolic conservation laws. Theodoros KATSAOUNIS. Doron LEVY
E COLE NORMALE SUPERIEURE A moded structured central scheme for 2D hyperbolc conservaton laws Theodoros KATSAOUNIS Doron LEVY LMENS - 98-30 Département de Mathématques et Informatque CNRS URA 762 A moded
More informationA Binarization Algorithm specialized on Document Images and Photos
A Bnarzaton Algorthm specalzed on Document mages and Photos Ergna Kavalleratou Dept. of nformaton and Communcaton Systems Engneerng Unversty of the Aegean kavalleratou@aegean.gr Abstract n ths paper, a
More informationR s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes
SPH3UW Unt 7.3 Sphercal Concave Mrrors Page 1 of 1 Notes Physcs Tool box Concave Mrror If the reflectng surface takes place on the nner surface of the sphercal shape so that the centre of the mrror bulges
More informationLearning the Kernel Parameters in Kernel Minimum Distance Classifier
Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and Zh-Hua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department
More informationA COMPARISON OF TWO METHODS FOR FITTING HIGH DIMENSIONAL RESPONSE SURFACES
Mam, Florda, U.S.A., Aprl 6-8, 7 A COMPARISON OF TWO METHODS FOR FITTING HIGH DIMENSIONAL RESPONSE SURFACES Marcelo J. Colaço Department of Mechancal and Materals Eng. Mltary Insttute of Engneerng Ro de
More informationHigh-Boost Mesh Filtering for 3-D Shape Enhancement
Hgh-Boost Mesh Flterng for 3-D Shape Enhancement Hrokazu Yagou Λ Alexander Belyaev y Damng We z Λ y z ; ; Shape Modelng Laboratory, Unversty of Azu, Azu-Wakamatsu 965-8580 Japan y Computer Graphcs Group,
More informationFeature Reduction and Selection
Feature Reducton and Selecton Dr. Shuang LIANG School of Software Engneerng TongJ Unversty Fall, 2012 Today s Topcs Introducton Problems of Dmensonalty Feature Reducton Statstc methods Prncpal Components
More informationNUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS
ARPN Journal of Engneerng and Appled Scences 006-017 Asan Research Publshng Network (ARPN). All rghts reserved. NUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS Igor Grgoryev, Svetlana
More informationParallelism for Nested Loops with Non-uniform and Flow Dependences
Parallelsm for Nested Loops wth Non-unform and Flow Dependences Sam-Jn Jeong Dept. of Informaton & Communcaton Engneerng, Cheonan Unversty, 5, Anseo-dong, Cheonan, Chungnam, 330-80, Korea. seong@cheonan.ac.kr
More informationWavefront Reconstructor
A Dstrbuted Smplex B-Splne Based Wavefront Reconstructor Coen de Vsser and Mchel Verhaegen 14-12-201212 2012 Delft Unversty of Technology Contents Introducton Wavefront reconstructon usng Smplex B-Splnes
More informationDynamic wetting property investigation of AFM tips in micro/nanoscale
Dynamc wettng property nvestgaton of AFM tps n mcro/nanoscale The wettng propertes of AFM probe tps are of concern n AFM tp related force measurement, fabrcaton, and manpulaton technques, such as dp-pen
More informationA High-Order Accurate Unstructured GMRES Solver for Poisson s Equation
A High-Order Accurate Unstructured GMRES Solver for Poisson s Equation Amir Nejat * and Carl Ollivier-Gooch Department of Mechanical Engineering, The University of British Columbia, BC V6T 1Z4, Canada
More informationOrder of Accuracy Study of Unstructured Grid Finite Volume Upwind Schemes
João Luz F. Azevedo et al. João Luz F. Azevedo joaoluz.azevedo@gmal.com Comando-Geral de Tecnologa Aeroespacal Insttuto de Aeronáutca e Espaço IAE 12228-903 São José dos Campos, SP, Brazl Luís F. Fguera
More informationOVERSET UNSTRUCTURED GRID METHOD FOR FLOW SIMULATION OF COMPLEX AND MULTIPLE BODY PROBLEMS
ICAS 2000 CONGRESS OVERSET UNSTRUCTURED GRID METHOD FOR FLOW SIMULATION OF COMPLEX AND MULTIPLE BODY PROBLEMS Kazuhro Nakahash, Fumya Togash Tohoku Unversty Keywords: CFD, Unstructured grd, overset grd
More information. Introducton. The system of unsteady compressble Naver-Stokes (N.-S.) equatons s a fundamental system n ud dynamcs. To be able to solve the system qu
VARIABLE DEGREE SCHWARZ METHODS FOR THE IMPLICIT SOLUTION OF UNSTEADY COMPRESSIBLE NAVIER-STOKES EQUATIONS ON TWO-DIMENSIONAL UNSTRUCTURED MESHES Xao-Chuan Ca y Department of Computer Scence Unversty of
More informationFair Triangle Mesh Generation with Discrete Elastica
Far Trangle Mesh Generaton wth Dscrete Elastca Shn Yoshzawa, and Alexander G. Belyaev, Computer Graphcs Group, Max-Planck-Insttut für Informatk, 66123 Saarbrücken, Germany Phone: [+49](681)9325-414 Fax:
More informationUniversität Stuttgart Direkte numerische Simulation von Strömungslärm in komplexen Geometrien
Unverstät Stuttgart Drekte numersche Smulaton von Strömungslärm n komplexen Geometren Claus-Deter Munz Gregor Gassner, Floran Hndenlang, Andreas Brkefeld, Andrea Beck, Marc Staudenmaer, Thomas Bolemann,
More informationProblem Definitions and Evaluation Criteria for Computational Expensive Optimization
Problem efntons and Evaluaton Crtera for Computatonal Expensve Optmzaton B. Lu 1, Q. Chen and Q. Zhang 3, J. J. Lang 4, P. N. Suganthan, B. Y. Qu 6 1 epartment of Computng, Glyndwr Unversty, UK Faclty
More informationQuality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation
Intellgent Informaton Management, 013, 5, 191-195 Publshed Onlne November 013 (http://www.scrp.org/journal/m) http://dx.do.org/10.36/m.013.5601 Qualty Improvement Algorthm for Tetrahedral Mesh Based on
More informationAn accelerated value/policy iteration scheme for the solution of DP equations
An accelerated value/polcy teraton scheme for the soluton of DP equatons Alessandro Alla 1, Maurzo Falcone 2, and Dante Kalse 3 1 SAPIENZA - Unversty of Rome, Ple. Aldo Moro 2, Rome, Italy alla@mat.unroma1.t
More informationHigh resolution 3D Tau-p transform by matching pursuit Weiping Cao* and Warren S. Ross, Shearwater GeoServices
Hgh resoluton 3D Tau-p transform by matchng pursut Wepng Cao* and Warren S. Ross, Shearwater GeoServces Summary The 3D Tau-p transform s of vtal sgnfcance for processng sesmc data acqured wth modern wde
More informationReview of approximation techniques
CHAPTER 2 Revew of appromaton technques 2. Introducton Optmzaton problems n engneerng desgn are characterzed by the followng assocated features: the objectve functon and constrants are mplct functons evaluated
More informationAccounting for the Use of Different Length Scale Factors in x, y and z Directions
1 Accountng for the Use of Dfferent Length Scale Factors n x, y and z Drectons Taha Soch (taha.soch@kcl.ac.uk) Imagng Scences & Bomedcal Engneerng, Kng s College London, The Rayne Insttute, St Thomas Hosptal,
More informationModeling of Airfoil Trailing Edge Flap with Immersed Boundary Method
Downloaded from orbt.dtu.dk on: Sep 27, 2018 Modelng of Arfol Tralng Edge Flap wth Immersed Boundary Method Zhu, We Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær Publshed n: ICOWEOE-2011 Publcaton date:
More informationCluster Analysis of Electrical Behavior
Journal of Computer and Communcatons, 205, 3, 88-93 Publshed Onlne May 205 n ScRes. http://www.scrp.org/ournal/cc http://dx.do.org/0.4236/cc.205.350 Cluster Analyss of Electrcal Behavor Ln Lu Ln Lu, School
More informationA fast algorithm for color image segmentation
Unersty of Wollongong Research Onlne Faculty of Informatcs - Papers (Arche) Faculty of Engneerng and Informaton Scences 006 A fast algorthm for color mage segmentaton L. Dong Unersty of Wollongong, lju@uow.edu.au
More informationSolitary and Traveling Wave Solutions to a Model. of Long Range Diffusion Involving Flux with. Stability Analysis
Internatonal Mathematcal Forum, Vol. 6,, no. 7, 8 Soltary and Travelng Wave Solutons to a Model of Long Range ffuson Involvng Flux wth Stablty Analyss Manar A. Al-Qudah Math epartment, Rabgh Faculty of
More informationSimulation of a Ship with Partially Filled Tanks Rolling in Waves by Applying Moving Particle Semi-Implicit Method
Smulaton of a Shp wth Partally Flled Tanks Rollng n Waves by Applyng Movng Partcle Sem-Implct Method Jen-Shang Kouh Department of Engneerng Scence and Ocean Engneerng, Natonal Tawan Unversty, Tape, Tawan,
More informationLecture 5: Multilayer Perceptrons
Lecture 5: Multlayer Perceptrons Roger Grosse 1 Introducton So far, we ve only talked about lnear models: lnear regresson and lnear bnary classfers. We noted that there are functons that can t be represented
More informationAn adaptive gradient smoothing method (GSM) for fluid dynamics problems
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluds 2010; 62:499 529 Publshed onlne 17 March 2009 n Wley InterScence (www.nterscence.wley.com)..2032 An adaptve gradent smoothng
More informationAn Iterative Solution Approach to Process Plant Layout using Mixed Integer Optimisation
17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 An Iteratve Soluton Approach to Process Plant Layout usng Mxed
More informationTHREE-DIMENSIONAL UNSTRUCTURED GRID GENERATION FOR FINITE-VOLUME SOLUTION OF EULER EQUATIONS
ICAS 2000 CONGRESS THREE-DIMENSIONAL UNSTRUCTURED GRID GENERATION FOR FINITE-VOLUME SOLUTION OF EULER EQUATIONS Karm Mazaher, Shahram Bodaghabad Sharf Unversty of Technology Keywords: Unstructured grd
More informationComplex Deformable Objects in Virtual Reality
Complex Deformable Obects n Vrtual Realty Young-Mn Kang Department of Computer Scence Pusan Natonal Unversty ymkang@pearl.cs.pusan.ac.kr Hwan-Gue Cho Department of Computer Scence Pusan Natonal Unversty
More informationA New Approach For the Ranking of Fuzzy Sets With Different Heights
New pproach For the ankng of Fuzzy Sets Wth Dfferent Heghts Pushpnder Sngh School of Mathematcs Computer pplcatons Thapar Unversty, Patala-7 00 Inda pushpndersnl@gmalcom STCT ankng of fuzzy sets plays
More informationc 2009 Society for Industrial and Applied Mathematics
SIAM J. MATRIX ANAL. APPL. Vol. 31, No. 3, pp. 1382 1411 c 2009 Socety for Industral and Appled Mathematcs SUPERFAST MULTIFRONTAL METHOD FOR LARGE STRUCTURED LINEAR SYSTEMS OF EQUATIONS JIANLIN XIA, SHIVKUMAR
More informationInverse Kinematics (part 2) CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Spring 2016
Inverse Knematcs (part 2) CSE169: Computer Anmaton Instructor: Steve Rotenberg UCSD, Sprng 2016 Forward Knematcs We wll use the vector: Φ... 1 2 M to represent the array of M jont DOF values We wll also
More informationStructured Grid Generation Via Constraint on Displacement of Internal Nodes
Internatonal Journal of Basc & Appled Scences IJBAS-IJENS Vol: 11 No: 4 79 Structured Grd Generaton Va Constrant on Dsplacement of Internal Nodes Al Ashrafzadeh, Razeh Jalalabad Abstract Structured grd
More informationComparison of h-, p- and hp-adaptation for convective heat transfer
Computatonal Methods and Expermental Measurements XIII 495 Comparson of h-, p- and hp-adaptaton for convectve heat transfer D. W. Pepper & X. Wang Nevada Center for Advanced Computatonal Methods, Unversty
More informationTime Integration Schemes in Dynamic Problems
Internatonal Workshop of Advanced Manufacturng and Automaton (IWAMA 016) Tme Integraton Schemes n Dynamc Problems Effect of Dampng on Numercal Stablty and Accuracy Ashsh Aeran and Hrpa G. Lemu Dept. Mechancal
More informationDetermining the Optimal Bandwidth Based on Multi-criterion Fusion
Proceedngs of 01 4th Internatonal Conference on Machne Learnng and Computng IPCSIT vol. 5 (01) (01) IACSIT Press, Sngapore Determnng the Optmal Bandwdth Based on Mult-crteron Fuson Ha-L Lang 1+, Xan-Mn
More informationFast Computation of Shortest Path for Visiting Segments in the Plane
Send Orders for Reprnts to reprnts@benthamscence.ae 4 The Open Cybernetcs & Systemcs Journal, 04, 8, 4-9 Open Access Fast Computaton of Shortest Path for Vstng Segments n the Plane Ljuan Wang,, Bo Jang
More informationComplex Numbers. Now we also saw that if a and b were both positive then ab = a b. For a second let s forget that restriction and do the following.
Complex Numbers The last topc n ths secton s not really related to most of what we ve done n ths chapter, although t s somewhat related to the radcals secton as we wll see. We also won t need the materal
More informationSimulation Based Analysis of FAST TCP using OMNET++
Smulaton Based Analyss of FAST TCP usng OMNET++ Umar ul Hassan 04030038@lums.edu.pk Md Term Report CS678 Topcs n Internet Research Sprng, 2006 Introducton Internet traffc s doublng roughly every 3 months
More informationImmersed Boundary Method for the Solution of 2D Inviscid Compressible Flow Using Finite Volume Approach on Moving Cartesian Grid
Journal of Appled Flud Mechancs, Vol. 4, No. 2, Specal Issue, pp. 27-36, 2011. Avalable onlne at www.jafmonlne.net, ISSN 1735-3572, EISSN 1735-3645. Immersed Boundary Method for the Soluton of 2D Invscd
More informationUrbaWind, a Computational Fluid Dynamics tool to predict wind resource in urban area
UrbaWnd, a Computatonal Flud Dynamcs tool to predct wnd resource n urban area Karm FAHSSIS a, Gullaume DUPONT a, Perre LEYRONNAS a a Meteodyn, Nantes, France Presentng Author: Karm.fahsss@meteodyn.com,
More informationAdaptive Fairing of Surface Meshes by Geometric Diffusion
Adaptve Farng of Surface Meshes by Geometrc Dffuson Chandrajt L. Bajaj Department of Computer Scences, Unversty of Texas, Austn, TX 78712 Emal: bajaj@cs.utexas.edu Guolang Xu State Key Lab. of Scentfc
More informationTsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance
Tsnghua Unversty at TAC 2009: Summarzng Mult-documents by Informaton Dstance Chong Long, Mnle Huang, Xaoyan Zhu State Key Laboratory of Intellgent Technology and Systems, Tsnghua Natonal Laboratory for
More informationSENSITIVITY ANALYSIS WITH UNSTRUCTURED FREE MESH GENERATORS IN 2-D AND 3-D SHAPE OPTIMIZATION.
SENSITIVITY ANALYSIS WITH UNSTRUCTURED FREE MESH GENERATORS IN 2-D AND 3-D SHAPE OPTIMIZATION. P. Duysnx, W.H. Zhang, C. Fleury. Aerospace Laboratory, LTAS, Unversty of Lège B-4000 LIEGE, BELGIUM. ABSTRACT.
More informationModeling, Manipulating, and Visualizing Continuous Volumetric Data: A Novel Spline-based Approach
Modelng, Manpulatng, and Vsualzng Contnuous Volumetrc Data: A Novel Splne-based Approach Jng Hua Center for Vsual Computng, Department of Computer Scence SUNY at Stony Brook Talk Outlne Introducton and
More informationAssignment # 2. Farrukh Jabeen Algorithms 510 Assignment #2 Due Date: June 15, 2009.
Farrukh Jabeen Algorthms 51 Assgnment #2 Due Date: June 15, 29. Assgnment # 2 Chapter 3 Dscrete Fourer Transforms Implement the FFT for the DFT. Descrbed n sectons 3.1 and 3.2. Delverables: 1. Concse descrpton
More informationProjection-Based Performance Modeling for Inter/Intra-Die Variations
Proecton-Based Performance Modelng for Inter/Intra-De Varatons Xn L, Jayong Le 2, Lawrence. Plegg and Andrze Strowas Dept. of Electrcal & Computer Engneerng Carnege Mellon Unversty Pttsburgh, PA 523, USA
More informationMesh Editing in ROI with Dual Laplacian
Mesh Edtng n ROI wth Dual Laplacan Luo Qong, Lu Bo, Ma Zhan-guo, Zhang Hong-bn College of Computer Scence, Beng Unversty of Technology, Chna lqngng@sohu.com, lubo@but.edu.cn,mzgsy@63.com,zhb@publc.bta.net.cn
More informationHelsinki University Of Technology, Systems Analysis Laboratory Mat Independent research projects in applied mathematics (3 cr)
Helsnk Unversty Of Technology, Systems Analyss Laboratory Mat-2.08 Independent research projects n appled mathematcs (3 cr) "! #$&% Antt Laukkanen 506 R ajlaukka@cc.hut.f 2 Introducton...3 2 Multattrbute
More informationRange images. Range image registration. Examples of sampling patterns. Range images and range surfaces
Range mages For many structured lght scanners, the range data forms a hghly regular pattern known as a range mage. he samplng pattern s determned by the specfc scanner. Range mage regstraton 1 Examples
More informationContent Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers
IOSR Journal of Electroncs and Communcaton Engneerng (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue, Ver. IV (Mar - Apr. 04), PP 0-07 Content Based Image Retreval Usng -D Dscrete Wavelet wth
More informationA mathematical programming approach to the analysis, design and scheduling of offshore oilfields
17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 A mathematcal programmng approach to the analyss, desgn and
More informationProper Choice of Data Used for the Estimation of Datum Transformation Parameters
Proper Choce of Data Used for the Estmaton of Datum Transformaton Parameters Hakan S. KUTOGLU, Turkey Key words: Coordnate systems; transformaton; estmaton, relablty. SUMMARY Advances n technologes and
More informationSubspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;
Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features
More informationModule 6: FEM for Plates and Shells Lecture 6: Finite Element Analysis of Shell
Module 6: FEM for Plates and Shells Lecture 6: Fnte Element Analyss of Shell 3 6.6. Introducton A shell s a curved surface, whch by vrtue of ther shape can wthstand both membrane and bendng forces. A shell
More informationPrivate Information Retrieval (PIR)
2 Levente Buttyán Problem formulaton Alce wants to obtan nformaton from a database, but she does not want the database to learn whch nformaton she wanted e.g., Alce s an nvestor queryng a stock-market
More informationDiscontinuous Galerkin methods for flow and transport problems in porous media
T COMMUNICATIONS IN NUMERICA METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2; :1 6 [Verson: 2/3/22 v1.] Dscontnuous Galerkn methods for flow and transport problems n porous meda Béatrve Rvère and Mary
More informationVISCOELASTIC SIMULATION OF BI-LAYER COEXTRUSION IN A SQUARE DIE: AN ANALYSIS OF VISCOUS ENCAPSULATION
VISCOELASTIC SIMULATION OF BI-LAYER COEXTRUSION IN A SQUARE DIE: AN ANALYSIS OF VISCOUS ENCAPSULATION Mahesh Gupta Mchgan Technologcal Unversty Plastc Flow, LLC Houghton, MI 49931 Hancock, MI 49930 Abstract
More informationNAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics
Introducton G10 NAG Fortran Lbrary Chapter Introducton G10 Smoothng n Statstcs Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Smoothng Methods... 2 2.2 Smoothng Splnes and Regresson
More informationNUMERICAL ANALYSIS OF A COUPLED FINITE-INFINITE ELEMENT METHOD FOR EXTERIOR HELMHOLTZ PROBLEMS
Journal of Computatonal Acoustcs, Vol. 14, No. 1 (2006) 21 43 c IMACS NUMERICAL ANALYSIS OF A COUPLED FINITE-INFINITE ELEMENT METHOD FOR EXTERIOR HELMHOLTZ PROBLEMS JEAN-CHRISTOPHE AUTRIQUE LMS Internatonal,
More informationHarmonic Coordinates for Character Articulation PIXAR
Harmonc Coordnates for Character Artculaton PIXAR Pushkar Josh Mark Meyer Tony DeRose Bran Green Tom Sanock We have a complex source mesh nsde of a smpler cage mesh We want vertex deformatons appled to
More informationCorner-Based Image Alignment using Pyramid Structure with Gradient Vector Similarity
Journal of Sgnal and Informaton Processng, 013, 4, 114-119 do:10.436/jsp.013.43b00 Publshed Onlne August 013 (http://www.scrp.org/journal/jsp) Corner-Based Image Algnment usng Pyramd Structure wth Gradent
More informationSENSITIVITY ANALYSIS IN LINEAR PROGRAMMING USING A CALCULATOR
SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING USING A CALCULATOR Judth Aronow Rchard Jarvnen Independent Consultant Dept of Math/Stat 559 Frost Wnona State Unversty Beaumont, TX 7776 Wnona, MN 55987 aronowju@hal.lamar.edu
More informationApplications of DEC:
Applcatons of DEC: Flud Mechancs and Meshng Dscrete Dfferental Geometry Overvew Puttng DEC to good use Fluds, fluds, fluds geometrc nterpretaton of classcal models dscrete geometrc nterpretaton new geometry-based
More informationAn Efficient Genetic Algorithm with Fuzzy c-means Clustering for Traveling Salesman Problem
An Effcent Genetc Algorthm wth Fuzzy c-means Clusterng for Travelng Salesman Problem Jong-Won Yoon and Sung-Bae Cho Dept. of Computer Scence Yonse Unversty Seoul, Korea jwyoon@sclab.yonse.ac.r, sbcho@cs.yonse.ac.r
More informationAnalysis of 3D Cracks in an Arbitrary Geometry with Weld Residual Stress
Analyss of 3D Cracks n an Arbtrary Geometry wth Weld Resdual Stress Greg Thorwald, Ph.D. Ted L. Anderson, Ph.D. Structural Relablty Technology, Boulder, CO Abstract Materals contanng flaws lke nclusons
More informationReading. 14. Subdivision curves. Recommended:
eadng ecommended: Stollntz, Deose, and Salesn. Wavelets for Computer Graphcs: heory and Applcatons, 996, secton 6.-6., A.5. 4. Subdvson curves Note: there s an error n Stollntz, et al., secton A.5. Equaton
More informationSolutions to Programming Assignment Five Interpolation and Numerical Differentiation
College of Engneerng and Coputer Scence Mechancal Engneerng Departent Mechancal Engneerng 309 Nuercal Analyss of Engneerng Systes Sprng 04 Nuber: 537 Instructor: Larry Caretto Solutons to Prograng Assgnent
More informationRelated-Mode Attacks on CTR Encryption Mode
Internatonal Journal of Network Securty, Vol.4, No.3, PP.282 287, May 2007 282 Related-Mode Attacks on CTR Encrypton Mode Dayn Wang, Dongda Ln, and Wenlng Wu (Correspondng author: Dayn Wang) Key Laboratory
More informationKiran Joy, International Journal of Advanced Engineering Technology E-ISSN
Kran oy, nternatonal ournal of Advanced Engneerng Technology E-SS 0976-3945 nt Adv Engg Tech/Vol. V/ssue /Aprl-une,04/9-95 Research Paper DETERMATO O RADATVE VEW ACTOR WTOUT COSDERG TE SADOWG EECT Kran
More information