In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.

Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid Integral equations in electromagnetics

A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.

Human exposure assessment in the near field of GSM base-station antennas using a hybrid finite element/method of moments technique

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

The SPEC High-Performance Group has developed the benchmark suite SPEC MPI2007 and its run rules over the last few years. The purpose of the SPEC MPI2007 benchmark and its run rules is to further the cause of fair and objective benchmarking of high-performance computing systems. The rules help to ensure that the published results are meaningful, comparable to other results, and reproducible. MPI2007 includes 13 technical computing applications from the fields of computational fluid dynamics, molecular dynamics, electromagnetism, geophysics, ray tracing, and hydrodynamics. We describe the benchmark suite, and compare it with other benchmark suites. Copyright © 2009 John Wiley & Sons, Ltd.

SPEC MPI2007—an application benchmark suite for parallel systems using MPI

The Factorized Sparse Approximate Inverse (FSAI) is an efficient technique for preconditioning parallel solvers of symmetric positive definite sparse linear systems. The key factor controlling FSAI efficiency is the identification of an appropriate nonzero pattern. Currently, several strategies have been proposed for building such a nonzero pattern, using both static and dynamic techniques. This article describes a fresh software package, called FSAIPACK, which we developed for shared memory parallel machines. It collects all available algorithms for computing FSAI preconditioners. FSAIPACK allows for combining different techniques according to any specified strategy, hence enabling the user to thoroughly exploit the potential of each preconditioner, in solving any peculiar problem. FSAIPACK is freely available as a compiled library at http://www.dmsa.unipd.it/~janna/software.html, together with an open-source command language interpreter. By writing a command ASCII file, one can easily perform and test any given strategy for building an FSAI preconditioner. Numerical experiments are discussed in order to highlight the FSAIPACK features and evaluate its computational performance.

FSAIPACK: A Software Package for High-Performance Factored Sparse Approximate Inverse Preconditioning

We develop a class of parallel multistep successive preconditioning strategies to enhance efficiency and robustness of standard sparse approximate inverse preconditioning techniques. The key idea is to compute a series of simple sparse matrices to approximate the inverse of the original matrix. Studies are conducted to show the advantages of such an approach in terms of both improving preconditioning accuracy and reducing computational cost, compared to the standard sparse approximate inverse preconditioners. Numerical experiments using one prototype implementation to solve a few sparse matrices on a distributed memory parallel computer are reported.

MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies

Global and localized parallel preconditioning techniques for large scale solid Earth simulations

http://www.cs.engr.uky.edu/~jzhang/pub/PRINT/shen5.pdf

Distributed block independent set algorithms and parallel multilevel ILU preconditioners

We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU)factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set algorithms and different coarse level solution strategies. We also use some diagonal thresholding and perturbation strategies to enhance factorization stability. Numerical experiments indicate that our parallel multilevel block ILU preconditioners are robust and efficient.

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Parallel multilevel block ILU preconditioning techniques for large sparse linear systems

Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems.

Kai Wang

Papers

MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies

Global and localized parallel preconditioning techniques for large scale solid Earth simulations

Distributed block independent set algorithms and parallel multilevel ILU preconditioners

Parallel multilevel block ILU preconditioning techniques for large sparse linear systems

A Comparative Study on Dynamic and Static Sparsity Patterns in Parallel Sparse Approximate Inverse Preconditioning