Generic Programming Experiments for SPn and SN transport codes
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1 Generic Programming Experiments for SPn and SN transport codes 10 mai 200 Laurent Plagne Angélique Ponçot Generic Programming Experiments for SPn and SN transport codes p1/26
2 Plan 1 Introduction How to write a good scientific code? 2 Neutron transport equations 3 Constraints/objectives for the library design 4 Generic Linear Algebra System Solver (GLASS) SPn code organization 6 Conclusion Success failure open questions Generic Programming Experiments for SPn and SN transport codes p2/26
3 How to write a good code? In an industrial context the ability to maintain the codes become essential Collaborative work is also a major issue How to separate the different scientific fields? Reactor Physics Numerical Analysis Computer Science Using libraries helps a lot Generic Programming Experiments for SPn and SN transport codes p3/26
4 $ Neutron transport equation! ( " # ) : Angular neutron flux Space : Energy : Angular direction : Generic Programming Experiments for SPn and SN transport codes p4/26
5 Sn discrete equations " 0 0!! X X X X X X X X X X X X X X X X Space Matrix Generic Programming Experiments for SPn and SN transport codes p/26
6 SPN equations (Mixed-Dual form) Pn Method : Angular Flux Legendre polynomials basis expansion The Simplified Pn method leads to : For each harmonic : Generic Programming Experiments for SPn and SN transport codes p6/26
7 Sn/SPn comparison l i l i g Sn g SPn h i h i Generic Programming Experiments for SPn and SN transport codes p/26
8 $ Stationnary Problem (criticality) One has to sove a generalized eigenvalue problem (SN/SPN) : Power algorithm :!#" Generic Programming Experiments for SPn and SN transport codes p8/26
9 $ Multigroup Equations One has to sove a linear problem (SN/SPN) : Gauss-Seidel algorithm : $! $! $!!#" Generic Programming Experiments for SPn and SN transport codes p9/26
10 SPn Matrix (A) A DSPNMatrix Diagonal (gg) + ScatteringMatrix Dense (gg ) MonoGroupMatrix DR + DMonogroupMatrix Diagonal RMonoGroupMatrix Dense ScatteringMonogroupMatrix Diagonal (hh) (hh ) (hh) DiffusionMatrix Special HarmonicCouplingMatrix Special SpaceScatteringMatrix Special Generic Programming Experiments for SPn and SN transport codes p10/26
11 !!! " " " GLASS : Main Constraints/Objectives and Vectors virtual/actual matrices matrix structure (sparsity pattern) hierarchy must be reflected (diagonal is a banded is a sparse is a dense) Blocked version of algorithms (Gauss-Seidel PowerAlgo) should be easy to read and write Flexibility to work for and from other codes ( No abstraction penalties The code should be easier to debug/maintain GLASS ) Generic Programming Experiments for SPn and SN transport codes p11/26
12 GLASS : Matrix Definition Concept A class matching the GLASS user concept is provided by the This class must contain all the information required to build evaluate matrix elements (Matrix sparsity pattern) (Type of matrix elements) A user defined class containing all the information required to build the matrix Depending on the provided the user must provide the corresponding static methods Generic Programming Experiments for SPn and SN transport codes p12/26
13 0 1 $ 1 1 $ " 1 $? 0 1? A 0 A 1 B 1?? example "! / - + )( $ # / + ( 2 "! ) $ ( ( ( $ # ( : : Generic Programming Experiments for SPn and SN transport codes p13/26
14 Example of use Generic Programming Experiments for SPn and SN transport codes p14/26
15 Matrix structures Hierachy DenseMatrix double operator () ( i j ) int nrows () int ncols() BandedMatrix double bandedgetelement( i j ) int nrows () int linf() int lsup () TriDiagonalMatrix double upperdiagonalgetelement( double lowerdiagonalgetelement( i ) double diagonalgetelement( i ) int nrows () DiagonalMatrix double diagonalgetelement( i ) int nrows () Generic Programming Experiments for SPn and SN transport codes p1/26
16 Nested Traits techniques DenseMatrix DenseMatrix BandedMatrix BandedMatrix TriDiagonalMatrix DiagonalMatrix TriDiagonalMatrix DiagonalMatrix Generic Programming Experiments for SPn and SN transport codes p16/26
17 Matrix options Generic Programming Experiments for SPn and SN transport codes p1/26
18 Matrix Options Generic Programming Experiments for SPn and SN transport codes p18/26
19 Algorithms How does the Gauss-Seidel algorithm look like? Generic Programming Experiments for SPn and SN transport codes p19/26
20 GLASS iterative solvers implementation : CONJUGATE GRADIENT ITERATIVE ALGORITHM JACOBI ITERATION CONTROL ACCELERATION METHOD SPACE KRYLOV METHOD TCHEBYCHEV ACCELERATION GAUSS SEIDEL AX B X Xold Generic Programming Experiments for SPn and SN transport codes p20/26
21 1 B " B # B 0 # B B 0 :??? GLASS iterative solvers implementation : / + 4 / " Generic Programming Experiments for SPn and SN transport codes p21/26
22 0 3 B # B? Iteration Control " / / 1 8 Generic Programming Experiments for SPn and SN transport codes p22/26
23 B B 0 3 B B? Acceleration Method " / / 4 # 4 / Generic Programming Experiments for SPn and SN transport codes p23/26
24 Solver organization SNSolver SPNSolver GLASS DiffusionMatrix SPNScatteringMatrix FissionMatrix GenericMatrix GenericVector GenericAlgos Generic Programming Experiments for SPn and SN transport codes p24/26
25 Performance comparison For the SPn approximation our reference is the MINOS code (C++) 3D IAEA benchmark The physical grid of size Calculation grid of size The benchmark implies 2 energy groups A simple SP1 approximation is used with linear finite elements The calculations were carried out on a 28 GHz Intel Xeon processor code Iteration Number EigenSolver duration (s) Minos s GLASS SPn s Generic Programming Experiments for SPn and SN transport codes p2/26
26 Conclusion Good Points Large fraction of codes shared between Sn and SPN No performance penalties Less bugs (no pointer much less loops -D BOUND CHECK) unitary tests Bad Points Error message handling for numerical analysis experts The code can t be read following your finger Some additionnal debugging tools should help (matrix browser) Still some work to handle certain temporary vectors new techniques new product Open question : What about //ism Generic Programming Experiments for SPn and SN transport codes p26/26
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