BIBLIOGRAPHY. Abramowicz, M., Stegun, I. A. (1964): Editors, Handbook of Mathematical Functions, Dover Publications.

Size: px

Start display at page:

Download "BIBLIOGRAPHY. Abramowicz, M., Stegun, I. A. (1964): Editors, Handbook of Mathematical Functions, Dover Publications."

Lynette Blake
5 years ago
Views:

1 BIBLIOGRAPHY Abramowicz, M., Stegun, I. A. (1964): Editors, Handbook of Mathematical Functions, Dover Publications. Argyris, J. H. (1954): Recent Advances in Matrix Method of Structural Analysis, Pergamon Press, Elmsford, New York. Bathe, K. J. (1982): Finite Element procedures in Engineering Analysis, Prentice Hall, Englewood Cliffs, New Jersey. Becker, E. B., Carey, G. F., Oden, J. T. (1981): Finite Elements - An Introduction, Vol. I, Prentice Hall, Englewood Cliffs, New Jersey. Beckers, M., Haegemans, A. (1991): The construction of three-dimensional invariant cubature formulae, Journal of Computational and Applied Mathematics, 35, Bernardini, F. (1991): Integration of polynomials over n-dimensional polyhedra, Computer Aided Design, 23, Bickford, W. B. (1990): A first course in the Finite Element Method, Irwin, Illinois. Brice Carnahan, Luther, H. A., James. O. Wilkes (1969): Applied Numerical Methods, John Wiley and sons. Burden, R. L., Faires, J. D. (1989): Numerical Analysis, 4 th Edn., PWS-Kent Publishing Company, Boston. Burnett, D. S. (1987): Finite Element Analysis: From Concepts to Applications, Addison Wesley Publ. Co., Reading, Massachusetts. Cattani, C., Paoluzzi, A. (1990): Boundary Integration over linear polyhedra, Computer Aided Design, 22, Cattani, C., Paoluzzi, A. (1990): Symbolic Analysis of Linear Polyhedra, Engineering with Computers, 6,

2 Cavendish, J. C., Gordon, W. J., Hall, C. A. (1976): Ritz-Galerkin approximation in bending function space, Numer. Math., 26, Chapra, S. C., Canale (2000): Numerical Methods for Science and Engineering Tata McGraw-Hill, New Delhi. Clough, R. W. (1960): The finite element in plane stress analysis, Proceedings of the 2 nd ASCE Conference on electronic computation, Pittsburgh, PA, Cook, R. D., Malkas, D. S., Plesha, M. E. (1988): Concepts and Applications of Finite Element Analysis. Cools, R. (1997): Constructing cubature formulae: the science behind the art, Acta Numerica, 6, Cools, R. (1999): Monomial cubature rules since Stroud : a compilation part 2, J. Comput. Appl. Math., 112, Cools, R. (2003): An encyclopedia of Cubature formulas, Journal of complexity, 19, Cools, R., Rabinowitz, P. (1993): Monomial cubature rules since Stroud: A compilation, Journal of Computational and Applied Mathematics, 48, Cowper, G. R. (1973): Gaussian quadrature formulas for triangles, Int. J. num. Meth. Engg., 7, Desai, C. S. (1979): Elementary Finite Element Method, Prentice Hall, Englewood Cliffs, New York. Dooren, P. V., Ridder, L. D. (1976): An adaptive algorithm for numerical integration over an n-dimensional cube, Journal of Computational and Applied Mathematics, 2, Dunavant, D. A. (1985): High degree efficient symmetrical Gaussian Quadrature Rules for the triangle, Int. J. Num. Meth. Engg., 21, Erwin Kreyszig (2001): Advanced Engineering Mathematics, 8 th Edn., John Wiley & Sons (ASIA) Pvt. Ltd. 150

3 Ethan J. Kubatko, Benjamin A. Yeager, Ashley L. Maggi (2013): New computationally efficient quadrature formulas for triangular prism elements, Computers & Fluids, 73, Ethan J. Kubatko, Benjamin A. Yeager, Ashley L. Maggi, Michael G. Duffy (2013): New computationally efficient quadrature formulas for pyramidal elements, Finite Elements in Analysis and Design, 65, Finlayson, B. A. (1972): The method of weighted residuals and variational principles with application in fluid mechanics, heat and mass transfer, Academic Press, New York. Gerald, C. F., Wheatley, P. O. (1999): Applied Numerical Analysis, 6 th Edn, Pearson Education, Asia. Grandin, H. Jr. (1986): Fundamentals of the Finite Element Method, Macmillan, New York. Hammer, P. C., Stroud, A. H. (1956): Numerical integration over simplexes, Math. Tables and other aids to computation, 10, Hammer, P. C., Stroud, A. H. (1958): Numerical Evaluation of multiple integrals, Math. Tables and other aids to computation, 12, Hammer, P. C., Marlowe, O. J., Stroud, A. H. (1956): Numerical integration over simplexes and cones, Math. Tables and other aids to computation, 10, Hildebrand, F. B. (1974): An introduction to numerical analysis, Tata McGraw Hill. Hillion, P. (1977): Numerical integration on a triangle, Int. J. num. Meth. Engg., 11, Huebner, K. H., Thornton, E. A. (1982): The Finite Element Method for Engineers, 2 nd ed., John Wiley, New York. Hughes, T. J. R. (1987): The Finite Element Method, Static and Dynamic Analysis, Prentice Hall, Englewood Cliffs, New Jersey. 151

4 Ichida, K., Kiyono, T. (1974): Numerical Integration in the irregular region, Computing, 12, Jain, R. K., Iyengar, S. R. K. (2002): Advanced Engineering Mathematics, Narosa Publishing House, New Delhi. James C. Cavendish, William J. Gordon, Charles A. Hall (1976): Ritz Galerkin approximations in blending function spaces, Numer. Math., 26, Karlin, S., Studden, W. (1966): Tchebycheff Systems with Applications in Analysis and Statistics, John Wiley (Interscience), New York. Lague, G., Baldur, R. (1977): Extended numerical integration method for triangular surfaces, Int. J. num. Meth. Engg., 11, Lannoy, F. G. (1977): Triangular finite elements and numerical integration, Computers & Structures, 7, 613. Laursen, M. E., Gellert, M. (1978): Some criteria for numerically integrated matrices and quadrature formulas for triangles, Int. J. num. Meth. Engg., 12, Laurie, D. P. (1977): Automatic numerical integration over a triangle, CSIR Spec. Rep. WISK 273, National Institute for Mathematical Sciences, Pretoria. Lee, Y. T., Requicha, A. A. G. (1982): Algorithms for computing the volume and other integral properties of solids I: known methods and open issues, Commun. ACM, 25, Lethor, F. G. (1976): Computation of double integrals over a triangle, J. Comp & Appl. Math., 2, Lewis, P. E., Ward, J. P. (1991): The Finite Element Method, Addison-Wesley, Reading, New York. Lien, S., Kajiya, J. T. (1984): A symbolic method for calculating the integral properties of arbitrary non convex polyhedra, IEEE Comput. Graph. Applic., 4,

5 Lyness, J. N., Jespersen, D. (1975): Moderate degree symmetric quadrature rules for the triangle, J. Inst. Math. Applic., 15, Ma, J., Rokhlin, V., Wandzura, S. (1996): Generalized Gaussian Quadrature rules for systems of arbitrary functions, SIAM J. Numer. Anal., 33, Michael G. Duffy (1982): Quadrature over a Pyramid or Cube of Integrands with a Singularity at a Vertex, SIAM J. Numer. Anal., 19, Mysovskikh, I. P. (1981): Interpolatory Cubature Formulas, Izdat, Nauka, Moscow, Leningrad (Russian). Piessens, R., de Doncker-Kapenga, E., Oberhuber, C. W., Kahaner, D. K. (1980): QUADBACK, a subroutine package for automatic integration Springer series in Computational Mathematics 1, Springer Verlag, Berlin, Heidelberg, New York, Tokyo. Rao, S. S. (1982): The Finite Element Method in Engineering, Pergamon, Oxford. Rathod, H. T., Govinda Rao, H. S. (1996): Integration of polynomials over an arbitrary tetrahedron in Euclidean Three-Dimensional Space, The Int. Journal of Computers & Structures, 59, Rathod, H. T., Hariprasad, A. S., Vijayakumar, K. V., Bharath Rathod, Nagabhushana, C. S. (2013): Numerical Integration over curved domain using convex quadrangulations and Gauss Legendre quadrature rules, 2, Rathod, H. T., Nagaraja, K. V., Venkatesudu, B., Ramesh, N. L. (2004): Gauss Legendre Quadrature over a Triangle, Journal of Indian Institute of Science, 84, Rathod, H. T., Shajedul Karim, M. D. (2002): An explicit integration scheme based on recursion for the curved triangular finite elements, Comput. Struct., 80, Rathod, H. T., Venkatesh, B. (2011): Gauss Legendre-Gauss Jacobi quadrature rules over a tetrahedral region, Int. Journal of Math. Analysis, 5,

6 Rathod, H. T., Venkatesudu, B., Nagaraja, K. V. (2005): Gauss Legendre quadrature formulas over tetrahedron, Numerical Methods for Partial Differential Equations, 22, Reddy, C. T. (1978): Improved three point integration schemes for triangular finite elements, Int. J. num. Meth. Engg., 12, Reddy, C. T., Shippy, D. J. (1981): Alternative integration formulae for triangular finite elements, Int. J. num. Meth. Engg., 17, Reddy, J. N. (1984): An introduction to the Finite Element Method, McGraw Hill Book Company, New York. Robin, J. Y., McLeod R. Murphy (1979): A Numerical comparison of high order transformation and isoparametric transformation methods, Comp. & Maths. with Appls., 5, Sag, T. W., Szekeras, G. (1964): Numerical Evaluation of High-Dimensional Integrals, Math. Comp., 18, Santin, G., Sommariva, A., Vianello, M. (2011): An algebraic cubature formula on curvilinear polygons, Applied Mathematics and Computation, 217, Shafiqul Islam Md., Alamgir Hossain, M. (2009): Numerical integrations over an arbitrary quadrilateral region, Applied Mathematics and Computation, 210, Sommariva, A., Vianello, M. (2006): Gauss Green cubature over spline curvilinear polygons, Applied Mathematics and Computation, 183, Sommariva, A., Vianello, M. (2009): Gauss Green cubature and moment computation over arbitrary geometries, Journal of Computational and Applied Mathematics, 231, Stroud, A.H., Secrest, D. (1966): Gaussian Quadrature Formulas, Prentice Hall Englewood Cliffs, New Jersey. 154

7 Stroud, A. H. (1971): Approximate Calculation of Multiple Integrals, Prentice Hall Englewood Cliffs, New Jersey. Sylvester, P. (1970): Symmetric Quadrature Formulae for Simplexes, Math. Comput., 24, Turner, M. J., Clough, R. W., Martin, H. C., Topp, L. J. (1956): Stiffness and deflection analysis of complex structures, J. Aero. Sci., 23, Wikipedia, The free Encyclopedia. Zienkiewicz, O. C. (1977): The Finite Element Method, McGraw Hill London, 3 rd Edn. Zienkiewicz, O. C., Cheung, Y. K. (1965): Finite elements in the solution of field problems, The Engineer, 220, Zienkiewicz, O. C., Taylor, R. L. (1989): The Finite Element Method Vol. I, International Edn., McGraw Hill London. Zienkiewicz, O. C., Taylor, R. L. (1991): The Finite Element Method, Vol. II, International Edn., McGraw Hill London. 155

Appropriate Gaussian quadrature formulae for triangles

International Journal of Applied Mathematics and Computation Journal homepage: www.darbose.in/ijamc ISSN: 097-665 (Print) 097-673 (Online) Volume (1) 01 3 Appropriate Gaussian quadrature formulae for triangles