Shared memory parallelism and low-rank approximation techniques applied to direct solvers in FEM simulation (regular paper)

In this paper, the performance of a parallel sparse direct solver on a shared-memory multicore system is presented. Large size test matrices arising from finite element simulation of induction heating industrial applications are used to evaluate the performance improvements due to low-rank representations and multicore parallelization.

[1]  F. Dughiero,et al.  A Translational Coupled Electromagnetic and Thermal Innovative Model for Induction Welding of Tubes , 2012, IEEE Transactions on Magnetics.

[2]  Mario Bebendorf,et al.  Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems , 2008 .

[3]  Patrick R. Amestoy,et al.  Improving Multifrontal methods by means of Low-Rank Approximations techniques , 2012 .

[4]  Takeshi Iwashita,et al.  A Fast Solver for FEM Analyses Using the , 2002 .

[5]  Fabrizio Dughiero,et al.  Multi-crystalline silicon ingots growth with an innovative induction heating directional solidification furnace , 2011, 2011 37th IEEE Photovoltaic Specialists Conference.

[6]  O. Bíró.  Edge element formulations of eddy current problems , 1999 .

[7]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2002, Future Gener. Comput. Syst..

[8]  Jianlin Xia,et al.  Superfast Multifrontal Method for Large Structured Linear Systems of Equations , 2009, SIAM J. Matrix Anal. Appl..

[9]  Patrick R. Amestoy,et al.  Grouping variables in Frontal Matrices to improve Low-Rank Approximations in a Multifrontal Solver , 2011 .

[10]  N. Takahashi,et al.  3-D Eddy Current Analysis of Induction Heating Apparatus Considering Heat Emission, Heat Conduction, and Temperature Dependence of Magnetic Characteristics , 2009, IEEE Transactions on Magnetics.

[11]  S. Börm.  Efficient Numerical Methods for Non-local Operators , 2010 .

[12]  Patrick R. Amestoy,et al.  Exploiting Multithreaded Tree Parallelism for Multicore Systems in a Parallel Multifrontal Solver , 2012 .