Accelerating the Multilevel Fast Multipole Algorithm with the Sparse-Approximate-Inverse (SAI) Preconditioning
Tahi dot,r Malas,Levent Gurel +2 more
TL;DR: This paper considers sparse approximate inverses generated from the sparse near-field part of the dense coefficient matrix, and proposes a load-balancing method to obtain high scalability during the setup phase.
read more
Abstract: With the help of the multilevel fast multipole algorithm, integral-equation methods can be used to solve real-life electromagnetics problems both accurately and efficiently. Increasing problem dimensions, on the other hand, necessitate effective parallel preconditioners with low setup costs. In this paper, we consider sparse approximate inverses generated from the sparse near-field part of the dense coefficient matrix. In particular, we analyze pattern selection strategies that can make efficient use of the block structure of the near-field matrix, and we propose a load-balancing method to obtain high scalability during the setup. We also present some implementation details, which reduce the computational cost of the setup phase. In conclusion, for the open-surface problems that are modeled by the electric-field integral equation, we have been able to solve ill-conditioned linear systems involving millions of unknowns with moderate computational requirements. For closed-surface problems that can be modeled by the combined-field integral equation, we reduce the solution times significantly compared to the commonly used block-diagonal preconditioner.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Solutions of large-scale electromagnetics problems using an iterative inner-outer scheme with ordinary and approximate multilevel fast multipole algorithms
TL;DR: The proposed iterative inner-outer scheme for the e-cient solution of large-scale electromagnetics problems involving perfectly- conducting objects formulated with surface integral equations shows that the processing time decreases significantly using the proposed method, compared to the solutions obtained with conventional preconditioners in the literature.
Sparse approximate inverse preconditioner for multiscale dynamic electromagnetic problems
Xiao-Min Pan,Xin-Qing Sheng +1 more
TL;DR: The proposed techniques include a skeleton‐based filtering strategy aiming to overcome the awkward filtering strategy extensively employed in traditional preconditioners and the strategy to recover the block structure of the inverse matrix.
39
Efficient Solutions of Metamaterial Problems Using a Low-Frequency Multilevel Fast Multipole Algorithm
Özgür Erguel,Levent Gurel +1 more
TL;DR: It is shown that the combination of an LF-MLFMA implementation based on the multipole expansion with the sparse-approximate-inverse preconditioner enables e-cient and ac- curate analysis of realistic metamaterial structures.
Schur Complement Preconditioners for Surface Integral-Equation Formulations of Dielectric Problems Solved with the Multilevel Fast Multipole Algorithm
Tahi dot,r Malas,Levent Gurel +2 more
TL;DR: The results for the photonic crystal problem shows that accurate CTF solutions for such problems can be obtained even faster than with second-kind integral equation formulations, with the acceleration provided by the proposed Schur complement preconditioners.
Efficient Analysis of Scattering by Multiple Moving Objects Using a Tailored MLFMA
TL;DR: A tailored multilevel fast multipole algorithm for efficient analysis of scattering by multiple moving objects and adopts the stationary grouping scheme in using the MLFMA for individual object, which is unchanged as the object is moving.
15
References
Parallel Preconditioning with Sparse Approximate Inverses
Marcus J. Grote,Thomas Huckle +1 more
TL;DR: A parallel preconditioner is presented for the solution of general sparse linear systems of equations using a sparse approximate inverse computed explicitly and then applied as a preconditionser to an iterative method.
702
Factorized sparse approximate inverse preconditionings I: theory
L. Yu. Kolotilina,A. Yu. Yeremin +1 more
TL;DR: This paper considers construction and properties of factorized sparse approximate inverse preconditionings well suited for implementation on modern parallel computers to preserve symmetry and/or positive definiteness of the original matrix and lead to convergent splittings.
396
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
Edmond Chow,Yousef Saad +1 more
TL;DR: Newton, "global," and column-oriented algorithms, and options for initial guesses, self-preconditioning, and dropping strategies are discussed, and some limited theoretical results on the properties and convergence of approximate inverses are derived.
309
Combining Fast Multipole Techniques and an Approximate Inverse Preconditioner for Large Electromagnetism Calculations
TL;DR: This paper designs an efficient parallelizable preconditioner that can be naturally implemented in a parallel code that implements the multipole technique for the matrix-vector product calculation and proposes an embedded iterative scheme that combines nested GMRES solvers with different fast multipole computations.
Analysis and performance of a distributed memory multilevel fast multipole algorithm
S. Velamparambil,Weng Cho Chew +1 more
TL;DR: The communication pattern and study the scalability of a distributed memory implementation of the multilevel fast multipole algorithm (MLFMA) called ScaleME, which uses the message passing interface (MPI) for communication between processors.
177