Optimizations of a fast multipole symmetric Galerkin boundary element method code

This paper presents some optimizations of a fast multipole symmetric Galerkin boundary element method code. Except general optimizations, the code is specially sped up for crack propagation problems. Existing useful computational results are saved and re-used during the propagation. Some time-consuming phases of the code are accelerated by a shared memory parallelization. A new sparse matrix method is designed based on coordinate format and compressed sparse row format to limit the memory required during the matrix construction phase. The remarkable performance of the new code is shown through many simulations including large-scale problems.

[1]  A. Brameller,et al.  Sparsity: Its practical application to systems analysis , 1976 .

[2]  Rohit Chandra,et al.  Parallel programming in openMP , 2000 .

[3]  Ross N. Adelman,et al.  FMM/GPU-Accelerated Boundary Element Method for Computational Magnetics and Electrostatics , 2017, IEEE Transactions on Magnetics.

[4]  V. Rokhlin Rapid solution of integral equations of classical potential theory , 1985 .

[5]  Attilio Frangi,et al.  3D fracture analysis by the symmetric Galerkin BEM , 2002 .

[6]  M. Bonnet,et al.  Solving multizone and multicrack elastostatic problems: A fast multipole symmetric Galerkin boundary element method approach , 2015 .

[7]  C. Balakrishna,et al.  Symmetric coupling of multi‐zone curved Galerkin boundary elements with finite elements in elasticity , 2000 .

[8]  S. Lie,et al.  Crack propagation analysis with Galerkin boundary element method , 2004 .

[9]  William Gropp,et al.  A Parallel Version of the Fast Multipole Method-Invited Talk , 1987, PPSC.

[10]  Martin Costabel,et al.  Symmetric Methods for the Coupling of Finite Elements and Boundary Elements (Invited contribution) , 1987 .

[11]  E. Schnack,et al.  Integration of singular Galerkin-type boundary element integrals for 3D elasticity problems , 1997 .

[12]  Frank J. Rizzo,et al.  On time-harmonic elastic-wave analysis by the boundary element method for moderate to high frequencies , 1986 .

[13]  B. H. Nguyen,et al.  Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems , 2017 .

[14]  Leonard J. Gray,et al.  Symmetric Galerkin boundary integral formulation for interface and multi-zone problems , 1997 .

[15]  Kenichi Yoshida,et al.  Applications of Fast Multipole Method to Boundary Integral Equation Method , 2001 .

[16]  A.-V. Phan,et al.  Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method , 2006 .

[17]  G. Novati,et al.  Weak Coupling of the Symmetric Galerkin BEM with FEM for Potential and Elastostatic Problems , 2006 .

[18]  Attila M. Zsaki,et al.  Accelerated parallel computation of field quantities for the boundary element method applied to stress analysis using multi-core CPUs, GPUs and FPGAs , 2018 .

[19]  L. Gray,et al.  SGBEM modeling of fatigue crack growth in particulate composites , 2010 .

[20]  R. Willoughby Sparse matrices and their applications , 1972 .

[21]  L. Gray,et al.  SGBEM for Cohesive Cracks in Homogeneous Media , 2010 .

[22]  B. H. Nguyen,et al.  An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems , 2016 .

[23]  A. Frangi Fracture propagation in 3D by the symmetric Galerkin boundary element method , 2002 .

[24]  Jacek Ptaszny,et al.  Parallel fast multipole boundary element method applied to computational homogenization , 2018 .

[25]  Youcef Saad,et al.  A Basic Tool Kit for Sparse Matrix Computations , 1990 .

[26]  S. Chaillat Fast Multipole Method for 3-D elastodynamic boundary integral equations. Application to seismic wave propagation , 2008 .

[27]  Yousef Saad,et al.  SPARK: a benchmark package for sparse computations , 1990, ICS '90.