A fast direct solver for periodic scattering problems for the Helmholtz equation in 2D

2014 ◽  
Vol 2014.27 (0) ◽  
pp. 307-309
Author(s):  
Yasuhiro MATSUMOTO ◽  
Kazuki NIINO ◽  
Naoshi NISHIMURA
Keyword(s):  
Helmholtz Equation ◽  
Scattering Problems ◽  
Direct Solver ◽  
Fast Direct Solver

scholarly journals An MPI-OpenMP Hybrid ParallelH-LU Direct Solver for Electromagnetic Integral Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Han Guo ◽  
Jun Hu ◽  
Zaiping Nie
Keyword(s):  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Message Passing ◽  
High Performance ◽  
Parallel Method ◽  
Scattering Problems ◽  
Direct Solver ◽  
3D Objects ◽  
Fast Solver ◽  
Fast Direct Solver

In this paper we propose a high performance parallel strategy/technique to implement the fast direct solver based on hierarchical matrices method. Our goal is to directly solve electromagnetic integral equations involving electric-large and geometrical-complex targets, which are traditionally difficult to be solved by iterative methods. The parallel method of our direct solver features both OpenMP shared memory programming and MPl message passing for running on a computer cluster. With modifications to the core direct-solving algorithm of hierarchical LU factorization, the new fast solver is scalable for parallelized implementation despite of its sequential nature. The numerical experiments demonstrate the accuracy and efficiency of the proposed parallel direct solver for analyzing electromagnetic scattering problems of complex 3D objects with nearly 4 million unknowns.

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