Parallel Iterative Methods with Factored Preconditioning Matrices for Solving Discrete Elliptic Equations

2004 ◽  
pp. 97-104 ◽  
Author(s):  
O.Yu. Milyukova
Keyword(s):  
Iterative Methods ◽  
Elliptic Equations ◽  
Parallel Iterative Methods ◽  
Parallel Iterative

Parallel Iterative Methods for the Helmholtz Equation With Exact Nonreflecting Boundaries

2002 ◽  
Author(s):  
Cristian Ianculescu ◽  
Lonny L. Thompson
Keyword(s):  
Helmholtz Equation ◽  
Iterative Methods ◽  
Scale Up ◽  
Low Rank ◽  
Interprocessor Communication ◽  
Parallel Iterative Methods ◽  
Local Boundary Condition ◽  
Non Local ◽  
Parallel Iterative ◽  
Low Rank Update

Parallel iterative methods for fast solution of large-scale acoustic radiation and scattering problems are developed using exact Dirichlet-to-Neumann (DtN), nonreflecting boundaries. A separable elliptic nonreflecting boundary is used to efficiently model unbounded regions surrounding elongated structures. We exploit the special structure of the non-local DtN map as a low-rank update of the system matrix to efficiently compute the matrix-by-vector products found in Krylov subspace based iterative methods. For the complex non-hermitian matrices resulting from the Helmholtz equation, we use a distributed-memory parallel BICG-STAB iterative method in conjunction with a parallel Jacobi preconditioner. Domain decomposition with interface minimization was performed to ensure optimal interprocessor communication. For the architectures tested, and using the MPICH version of MPI, we show that when implemented as a low-rank update, the non-local character of the DtN map does not signicantly decrease the scale up and parallel eciency versus a purely approximate local boundary condition.

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