Piotr Sypek

How to Render FDTD Computations More Effective Using a Graphics Accelerator

Graphics processing units (GPUs) for years have been dedicated mostly to real time rendering. Recently leading GPU manufactures have extended their research area and decided to support also graphics computing. In this paper, we describe an impact of new GPU features on development process of an efficient finite difference time domain (FDTD) implementation.

Finite Element Matrix Generation on a GPU

This paper presents an e-cient technique for fast gener- ation of sparse systems of linear equations arising in computational electromagnetics in a flnite element method using higher order ele- ments. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The per- formance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core Opterons), indicate that the GPU implementation of the matrix generation allows one to achieve speedups by a factor of 81 and 19 over the optimized single- and multi-threaded CPU-only implementations, respectively.

Accuracy, Memory, and Speed Strategies in GPU-Based Finite-Element Matrix-Generation

This letter presents strategies on how to optimize graphics processing unit (GPU)-based finite-element matrix-generation that occurs in the finite element method (FEM) using higher-order curvilinear elements. The goal of the optimization is to increase the speed of evaluation and assembly of large finite-element matrices on a single GPU while maintaining the accuracy of numerical integration at the desired level. For this reason, the choice of the optimal Gaussian quadratures for curvilinear finite elements focused on accuracy, memory usage, and runtime of numerical integration is discussed. Moreover, we show how to efficiently utilize symmetry of local mass and stiffness matrices on a GPU in the numerical integration step. The performance results, obtained on a workstation equipped with one Tesla C2075, indicate that the proposed strategies retain the accuracy of computations, allow generation of larger sparse linear systems, and provide 2.5-fold acceleration of GPU-based finite-element matrix-generation.

FDTD Analysis of EBG Structures with Macromodel Cloning

We propose an improved macromodel-based technique for efficient analysis of EBG structures in the finite difference time domain (FDTD) scheme. The technique involves macromodel symmetrization and diagonalization as well as cloning hundreds or even thousands of macromodels along the FDTD grid. The improved FDTD-macromodel scheme allows one to use macromodels on a large scale within the computation grid. Numerical results show that a high resolution analysis of EBG structures can be performed in time comparable to the coarse mesh FDTD simulation

Model order reduction for subgriddding in FDTD scheme

In this paper we present a technique for achieving high resolution in the FDTD. The technique combines model order reduction with subgridding. Such a combination allows one to condense mesh locally and get accurate results using limited number of variables. Moreover the overall time discretization step is longer than in case of the subgridding only. This enables one to perform the simulation quicker than in other schemes where fine mesh is used. The methodology of FDTD-macromodel scheme is demonstrated using a numerical example

Low Reflection Macromodels for a Stable FDTD Scheme Operating with Highly Refined Local Meshes

We propose a new technique of incorporat- ing macromodels into the Finite Difference Time Domain (FDTD) analysis. The technique involves combining grids with drastically different mesh densities and relies on a new interpolation algorithm which guarantees that macromodels incorporated into a standard FDTD scheme are both stable and do not cause reflections that decrease the accuracy. The proposed algorithm gives high accuracy and allows one to locally increase the grid resolution up to several orders of magnitude without significant time step reduction as illustrated on analyzed examples.

GPU-Accelerated Finite-Element Matrix Generation for Lossless, Lossy, and Tensor Media [EM Programmer's Notebook]

This paper presents an optimization approach for limiting memory requirements and enhancing the performance of GPU-accelerated finite-element matrix generation applied in the implementation of the higher-order finite-element method (FEM). It emphasizes the details of the implementation of the matrix-generation algorithm for the simulation of electromagnetic wave propagation in lossless, lossy, and tensor media. Moreover, the impact of GPU RAM memory requirements on the performance of the finite-element matrix-generation process is discussed. The numerical results were obtained using a workstation equipped with a Tesla K40 GPU and two Intel Xeon Sandy Bridge E5-2687W CPUs. The results obtained for the high-end test platform indicated that the utilization of a GPU in the finite-element matrix-generation process allowed significant time reduction. With double-precision arithmetic, the GPU-accelerated matrix generation of over 5 million unknowns could be carried out in a matter of tens of seconds, as opposed to a CPU that required several minutes.

Communication and Load Balancing Optimization for Finite Element Electromagnetic Simulations Using Multi-GPU Workstation

This paper considers a method for accelerating finite-element simulations of electromagnetic problems on a workstation using graphics processing units (GPUs). The focus is on finite-element formulations using higher order elements and tetrahedral meshes that lead to sparse matrices too large to be dealt with on a typical workstation using direct methods. We discuss the problem of rapid matrix generation and assembly, as well as accelerating preconditioned iterative solvers in the context of limited on-board GPU memory, and we show how to mitigate some of these problems using multiple GPUs. We propose a new fast data-distribution technique for multi-GPU platforms that allows optimal splitting of finite-element method (FEM) matrices between graphics accelerators. The technique draws upon the graph partitioning approach used in nonoverlapping domain-decomposition methods and provides information that drives the FEM matrix-generation and assembly process in such a way that it produces data structures for each GPU; this not only ensures load balancing and minimizes communication between GPUs, but also reflects the hierarchy of the basis functions. The concepts proposed in this paper are illustrated with examples involving sparse matrices of up to 13.9 million rows and over a billion nonzero elements.

Parallel Implementation of the Matrix Formulation of the FDTD Scheme

We present a scalable method for efficient implementation of matrix formulation for finite difference time domain (FDTD) algorithm on parallel architectures. The matrix definition based on physical data properties and data division among grid nodes yielding minimal data transfer between them is described. Numerical performance is evaluated in the heterogeneous grid environment and two clusters.

Object oriented grid computing for computational electromagnetics

We present WiCommGrid Java library that enables grid computing for heterogeneous hardware and software environment. Designed flexible data exchange mechanism can be easily incorporated to the extended program class hierarchy with no special treatment. Developed library is strongly encapsulated and almost transparent to wide range of program types. The application of the library in computational electromagnetics is illustrated on a ray tracing algorithm for indoor propagation simulation.