Parallel Multilevel Fast Multipole Algorithm Research Articles

High-Performance Evaluation of the Interpolations and Anterpolations in the GPU-Accelerated Massively Parallel MLFMA

This communication investigates high-performance computation schemes for local Lagrange interpolation and anterpolation operations in the parallel graphics processing unit (GPU)-accelerated distributed-memory multilevel fast multipole algorithm (MLFMA). Two ELLPACK format-based schemes, namely, block ELLPACK (ELL-B) and hybrid compressed sparse column (CSC)-block ELLPACK (CSC-ELL-B), are proposed for the evaluation of interpolation and anterpolation operations, respectively, which ensure high computational throughput for GPU calculation. Optimization using the GPU hierarchical memory architecture, the mechanism of the stream and the CPU/GPU asynchronous computation pattern are employed to further improve the overall performance. The proposed schemes are proven to be an order of magnitude faster than the conventional schemes for aggregation/disaggregation operations. For an aircraft model involving over 10 billion unknowns, the iteration time is reduced by over half, which is remarkable progress in the development of GPU-accelerated parallelization of MLFMA.

An Efficient Parallel Hybrid Method of FEM-MLFMA for Electromagnetic Radiation and Scattering Analysis of Separated Objects

In order to meet the rapidly increasing demand for accurate and efficient analysis of complex radiating or scattering structures in the presence of electrically large objects, a finite element method (FEM)-multilevel fast multipole algorithm (MLFMA) hybrid method that based on the Finite Element-Iterative Integral Equation Evaluation (FE-IIEE) mesh truncation technique is proposed in this paper. The present method makes use of FEM for the regions with small and complex features and MLFMA for the analysis of the electrically large objects, which ensure the accuracy and applicability of the method are better than most commonly adopted FEM-high frequency technique (HFT) hybrid method. The mutual interactions between regions are taken into account in a fully coupled way through iterative near filed computation process. In order to achieve an excellent performance, both algorithms have been implemented together from scratch, being able to run over multi CPU cores. An efficient parallel FEM domain decomposition method (DDM) solver with exploiting geometrical repetitions is included to drastically reduce memory requirements and computational time in the calculation of large array antenna. Also, the parallel MLFMA is adopted to expedite the near-field information exchange between regions. Through numerical example, the effect of distance between regions on the convergence of the proposed hybrid method is studied, and it is shown that the proposed method converge well even if the distance is equal to 0.05λ. Through comparisons with an in-house higher order method of moments (HOMoM) code and commercial software FEKO, the accuracy and effectiveness of the implemented parallel hybrid method are validated showing excellent performance.

Parallel Wideband MLFMA for Analysis of Electrically Large, Nonuniform, Multiscale Structures

Electromagnetic scattering from electrically large objects with multiscale features is an increasingly important problem in computational electromagnetics. A conventional approach is to use an integral equation-based solver that is then augmented with an accelerator, a popular choice being a parallel multilevel fast multipole algorithm (MLFMA). One consequence of multiscale features is locally dense discretization, which leads to low-frequency breakdown and requires nonuniform trees. To the authors' knowledge, the literature on parallel MLFMA for such multiscale distributions capable of arbitrary accuracy is sparse; this paper aims to fill this niche. We prescribe an algorithm that overcomes this bottleneck. We demonstrate the accuracy (with respect to analytical data) and performance of the algorithm for both PEC scatterers and point clouds as large as 755λ with several hundred million unknowns and nonuniform trees as deep as 16 levels.

Parallel Integral Equation-Based Nonoverlapping DDM for Solving Challenging Electromagnetic Scattering Problems of Two Thousand Wavelengths

In this paper, a parallel nonoverlapping and nonconformal domain decomposition method (DDM) is proposed for fast and accurate analysis of electrically large objects in the condition of limited resources. The formulation of nonoverlapping DDM for PEC bodies is derived from combined-field integral equation (CFIE), and an explicit boundary condition is applied to ensure the continuity of electric currents across the boundary. A parallel multilevel fast multipole algorithm (MLFMA) is extended to accelerate matrix-vector multiplications of subdomains as well as the coupling between them, and the coupling between different subdomains is computed in the manner of near field to avoid the storage of the mutual impedance. An improved adaptive direction partitioning scheme is applied to the oct-tree of MLFMA to achieve high parallel efficiency. Numerical examples demonstrate that the proposed method is able to simulate realistic problems with a maximum dimension greater than 2000 wavelengths.

Wide Angular Sweeping of Dynamic Electromagnetic Responses From Large Targets by MPI Parallel Skeletonization

It has been revealed that the interpolative decomposition (ID) skeletonization can greatly accelerate the wide angular sweeping, which involves repeatedly solving many/massive incidents. However, the peak memory usage required by skeletonization may be a bottleneck of that algorithm. In this communication, a message passing interface parallel skeletonization scheme is developed to alleviate the memory usage and to incorporate with the parallel multilevel fast multipole algorithm (MLFMA) for large targets, which are hundreds of wavelengths in size. The parallel scheme includes two ingredients. One is to feed into the ID, a size-reduced matrix to find skeleton right-hand sides. This matrix is produced upon skeleton RWGs instead of their original counterpart. The other is to integrate the parallel ID into the parallel MLFMA to alleviate the peak memory usage of skeletonization on each participating process. Numerical experiments show that the peak memory usage for the skeletonization can be less than 2 GB in each process for the target about 300 wavelengths in size.

Accurate and Efficient Simulation Model for the Scattering From a Ship on a Sea-Like Surface

An accurate and efficient simulation model is developed for the scattering from a 3-D ship on a 2-D sea-like surface. The ship on the sea-like surface is modeled as a ship on a random surface with the impedance boundary condition. A full-wave simulation method is developed to simulate this model by using the self-dual integral equation and the parallel multilevel fast multipole algorithm. The simulation model is compared with the model of a ship on a flat surface and on a perfectly electrically conducting random surface, respectively. The application ranges of these models are concluded. Furthermore, the characteristics of the ship on a sea-like surface are studied by using the developed simulation model.

Comparison of scattering diagrams of large non-spherical particles calculated by VCRM and MLFMA

The vectorial complex ray model (VCRM) developed in recent years improves considerably the precision and the applicability of the ray model in the light scattering by large non-spherical particles. But its results for particles of complex shape remain to be validated. The surface integral equation (SIE) with parallel multilevel fast multipole algorithm (MLFMA) is a rigorous numerical method so it permits us to obtain accurate results of particles of any shape. With new improvement we have made, our parallelized code of MLFMA allows us to calculate the scattering of non-spherical dielectric particles of size much larger than the incident wavelength. This paper is devoted to the validation of the VCRM by comparison of the scattering diagrams with the MLFMA results. The scattering diagrams of large ellipsoidal particles with different size parameters and aspect ratios are computed by using the two methods. Good agreements between them prove the ability of both MLFMA and VCRM for large non-spherical particles.

A Well-Scaling Parallel Algorithm for the Computation of the Translation Operator in the MLFMA

This paper investigates the parallel, distributed-memory computation of the translation operator with L+1 multipoles in the three-dimensional Multilevel Fast Multipole Algorithm (MLFMA). A baseline, communication-free parallel algorithm can compute such a translation operator in O(L) time, using O(L2) processes. We propose a parallel algorithm that reduces this complexity to O(logL) time. This complexity is theoretically supported and experimentally validated up to 16 384 parallel processes. For realistic cases, the implementation of the proposed algorithm proves to be up to ten times faster than the baseline algorithm. For a large-scale parallel MLFMA simulation with 4096 parallel processes, the runtime for the computation of all translation operators during the setup stage is reduced from roughly one hour to only a few minutes.

Weak Scalability Analysis of the Distributed-Memory Parallel MLFMA

Distributed-memory parallelization of the multilevel fast multipole algorithm (MLFMA) relies on the partitioning of the internal data structures of the MLFMA among the local memories of networked machines. For three existing data partitioning schemes (spatial, hybrid and hierarchical partitioning), the weak scalability, i.e., the asymptotic behavior for proportionally increasing problem size and number of parallel processes, is analyzed. It is demonstrated that none of these schemes are weakly scalable. A nontrivial change to the hierarchical scheme is proposed, yielding a parallel MLFMA that does exhibit weak scalability. It is shown that, even for modest problem sizes and a modest number of parallel processes, the memory requirements of the proposed scheme are already significantly lower, compared to existing schemes. Additionally, the proposed scheme is used to perform full-wave simulations of a canonical example, where the number of unknowns and CPU cores are proportionally increased up to more than 200 millions of unknowns and 1024 CPU cores. The time per matrix-vector multiplication for an increasing number of unknowns and CPU cores corresponds very well to the theoretical time complexity.

Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm

Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver.

Accurate solutions of extremely large integral-equation problems in computational electromagnetics

Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknowns. Some of the complicated real-life problems (such as scattering from a realistic aircraft) involve geometries that are larger than 1000 wavelengths. Accurate solutions of such problems can be used as benchmarking data for many purposes and even as reference data for high-frequency techniques. Solutions of extremely large canonical benchmark problems involving sphere and National Aeronautics and Space Administration (NASA) Almond geometries are presented, in addition to the solution of complicated objects, such as the Flamme. The parallel implementation is also extended to solve very large dielectric problems, such as dielectric lenses and photonic crystals.

Automatic Load-Balanced Partitioning Strategy in Parallel Multilevel Fast Multipole Algorithm

In this paper, we propose an automatic load-balanced partitioning strategy for parallel multilevel fast multipole algorithm(MLFMA) based on distributed-memory architectures to solve the large scale electromagnetic scattering problems. We focus on the automatic load-balancing partitioning strategy because that our original scheme requires that users input the transition level, which is usually determined on the users’ experience and sometimes lead to a bad load-balancing partition. By introducing the automatic load-balancing algorithm to our pervious partitioning technique, our implementation can automatically achieve the best load-balancing and consequently attain better parallel efficiency. To present the effectiveness of the new strategy, we analyze results of the previous implementation according to different inputs of transition level and compare them with the result of implementation using the new algorithm.

Solving Problems With Over One Billion Unknowns by the MLFMA

Using OpenMP to further accelerate the pure MPI parallel MLFMA, an efficient and flexible parallel multilevel fast multipole algorithm (MPI-OpenMP-MLFMA) is proposed. Compared with previous MPI parallel schemes, the MPI-OpenMP-MLFMA improves the load-balance and scalability greatly. The computational capability of the proposed MPI-OpenMP-MLFMA is demonstrated by computing scattering from two extremely large targets: a sphere with a diameter of 1200 wavelengths, modeled by 1,063,706,700 unknowns, and an airplane model with the largest dimension of 1600 wavelengths, involving 288,151,344 unknowns.

Inplementation of an Efficient Parallel Multilevel Fast Multipole Algorithm

This paper is concerned with the implementation of the parallel multilevel fast multipole algorithm(MLFMA) for large scale electromagnetics simulation on shared-memory system. The algorithm is implemented on a method of moment discretisation of the electromagnetics scattering problems.The developed procesure is validated by compared to benchmarks defined by Electromagnetics Code Consortium(EMCC) .The procesure can evaluate large problemssuch as electromagnetics scattering of aircraft at high-frequency with up to several millions of unknowns.

A fast 2‐D parallel multilevel fast multipole algorithm solver for oblique plane wave incidence

We present a multilevel fast multipole algorithm (MLFMA) implementation to numerically solve Maxwell's equations for large two‐dimensional geometries illuminated by an arbitrary plane wave in three‐dimensional space. The solver's capabilities are augmented by means of an asynchronous and hierarchical parallelization. Its accuracy is demonstrated by comparing the analytical and numerically obtained scattering width of several canonical examples with a size of 700,000 wavelengths.

Solutions of large-scale electromagnetics problems involving dielectric objects with the parallel multilevel fast multipole algorithm

Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao-Wilton-Glisson functions. Solutions are performed iteratively by using the multilevel fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures using a rigorous technique, namely, the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large problems involving as many as 100 million unknowns.

Improvement and performance of parallel multilevel fast multipole algorithm

Improvement and performance of parallel multilevel fast multipole algorithm

ON OPENMP PARALLELIZATION OF THE MULTILEVEL FAST MULTIPOLE ALGORITHM

Compared with MPI, OpenMP provides us an easy way to parallelize the multilevel fast multipole algorithm (MLFMA) on shared-memory systems. However, the implementation of OpenMP parallelization has many pitfalls because difierent parts of MLFMA have distinct numerical characteristics due to its complicated algorithm structure. These pitfalls often cause very low e-ciency, especially when many threads are employed. Through an in-depth investigation on these pitfalls with analysis and numerical experiments, we propose an e-cient OpenMP parallel MLFMA. Two strategies are proposed in the parallelization, including: 1) loop reorganization for far-fleld interaction in the MLFMA; 2) determination of a transition level. Numerical experiments on large scale targets show the proposed OpenMP parallel scheme can perform as e-ciently as the MPI counterpart, and much more e-ciently than the straightforward OpenMP parallel one.

Improving Iterative Solutions of the Electric-Field Integral Equation Via Transformations Into Normal Equations

We consider the solution of electromagnetics problems involving perfectly conducting objects formulated with the electric-field integral equation (EFIE). Dense matrix equations obtained from the discretization of EFIE are solved iteratively by the generalized minimal residual (GMRES) algorithm accelerated with a parallel multilevel fast multipole algorithm. We show that the number of iterations is halved by transforming the original matrix equations into normal equations. This way, memory required for the GMRES algorithm is reduced by more than 50%, which is significant when the problem size is large.

Full-wave electromagnetic scattering at extremely large 2-D objects

Recent advances in the parallel multilevel fast multipole algorithm have paved the way for large-scale full-wave electromagnetic simulations. The introduction of the hierarchical partitioning technique and the use of an asynchronous parallel implementation have resulted in a scalable algorithm that runs efficiently, even on low-cost clusters. Presented is the accurate solution of the two-dimensional (2-D) transverse magnetic scattering at both a perfect electric conducting cylinder with a diameter of one million wavelengths and a dielectric cylinder with a diameter of half a million wavelengths.