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Wyniki wyszukiwania dla: GENERALIZED EIGENVALUE PROBLEM, FEM, COMPLEX-VALUED SPARSE MATRIX PENCIL, GPU, MAXWELL’S EQUATIONS.
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A GPU Solver for Sparse Generalized Eigenvalue Problems with Symmetric Complex-Valued Matrices Obtained Using Higher-Order FEM
PublikacjaThe paper discusses a fast implementation of the stabilized locally optimal block preconditioned conjugate gradient (sLOBPCG) method, using a hierarchical multilevel preconditioner to solve nonHermitian sparse generalized eigenvalue problems with large symmetric complex-valued matrices obtained using the higher-order finite-element method (FEM), applied to the analysis of a microwave resonator. The resonant frequencies of the low-order...
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A memory efficient and fast sparse matrix vector product on a Gpu
PublikacjaThis paper proposes a new sparse matrix storage format which allows an efficient implementation of a sparse matrix vector product on a Fermi Graphics Processing Unit (GPU). Unlike previous formats it has both low memory footprint and good throughput. The new format, which we call Sliced ELLR-T has been designed specifically for accelerating the iterative solution of a large sparse and complex-valued system of linear equations arising...
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Block Conjugate Gradient Method with Multilevel Preconditioning and GPU Acceleration for FEM Problems in Electromagnetics
PublikacjaIn this paper a GPU-accelerated block conjugate gradient solver with multilevel preconditioning is presented for solving large system of sparse equations with multiple right hand-sides (RHSs) which arise in the finite-element analysis of electromagnetic problems. We demonstrate that blocking reduces the time to solution significantly and allows for better utilization of the computing power of GPUs, especially when the system matrix...
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Single and Dual-GPU Generalized Sparse Eigenvalue Solvers for Finding a Few Low-Order Resonances of a Microwave Cavity Using the Finite-Element Method
PublikacjaThis paper presents two fast generalized eigenvalue solvers for sparse symmetric matrices that arise when electromagnetic cavity resonances are investigated using the higher-order finite element method (FEM). To find a few loworder resonances, the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm with null-space deflation is applied. The computations are expedited by using one or two graphical processing...
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Tuning matrix-vector multiplication on GPU
PublikacjaA matrix times vector multiplication (matvec) is a cornerstone operation in iterative methods of solving large sparse systems of equations such as the conjugate gradients method (cg), the minimal residual method (minres), the generalized residual method (gmres) and exerts an influence on overall performance of those methods. An implementation of matvec is particularly demanding when one executes computations on a GPU (Graphics...
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GPU-accelerated finite element method
PublikacjaIn this paper the results of the acceleration of computations involved in analysing electromagnetic problems by means of the finite element method (FEM), obtained with graphics processors (GPU), are presented. A 4.7-fold acceleration was achieved thanks to the massive parallelization of the most time-consuming steps of FEM, namely finite-element matrix-generation and the solution of a sparse system of linear equations with the...
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Preconditioners with Low Memory Requirements for Higher-Order Finite-Element Method Applied to Solving Maxwell’s Equations on Multicore CPUs and GPUs
PublikacjaThis paper discusses two fast implementations of the conjugate gradient iterative method using a hierarchical multilevel preconditioner to solve the complex-valued, sparse systems obtained using the higher order finite-element method applied to the solution of the time-harmonic Maxwell equations. In the first implementation, denoted PCG-V, a classical V-cycle is applied and the system of equations on the lowest level is solved...
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Tuning a Hybrid GPU-CPU V-Cycle Multilevel Preconditioner for Solving Large Real and Complex Systems of FEM Equations
PublikacjaThis letter presents techniques for tuning an accelerated preconditioned conjugate gradient solver with a multilevel preconditioner. The solver is optimized for a fast solution of sparse systems of equations arising in computational electromagnetics in a finite element method using higher-order elements. The goal of the tuning is to increase the throughput while at the same time reducing the memory requirements in order to allow...
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A Task-Scheduling Approach for Efficient Sparse Symmetric Matrix-Vector Multiplication on a GPU
PublikacjaIn this paper, a task-scheduling approach to efficiently calculating sparse symmetric matrix-vector products and designed to run on Graphics Processing Units (GPUs) is presented. The main premise is that, for many sparse symmetric matrices occurring in common applications, it is possible to obtain significant reductions in memory usage and improvements in performance when the matrix is prepared in certain ways prior to computation....
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Implementation of algebraic procedures on the GPU using CUDA architecture on the example of generalized eigenvalue problem
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Finite element matrix generation on a GPU
PublikacjaThis paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The performance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core...
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GPU-Accelerated LOBPCG Method with Inexact Null-Space Filtering for Solving Generalized Eigenvalue Problems in Computational Electromagnetics Analysis with Higher-Order FEM
PublikacjaThis paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact nullspace filtering approach to find eigenvalues in electromagnetics analysis with higherorder FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from...
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GENERAL DYNAMIC PROJECTING OF MAXWELL EQUATIONS
PublikacjaA complete – system of Maxwell equations is splitting into independent subsystems by means of a special dynamic projecting technique. The technique relies upon a direct link between field components that determine correspondent subspaces. The explicit form of links and corresponding subspace evolution equations are obtained in conditions of certain symmetry, it is illustrated by examples of spherical and quasi-one-dimensional waves.
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Accuracy, Memory and Speed Strategies in GPU-based Finite-Element Matrix-Generation
PublikacjaThis paper presents strategies on how to optimize 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 (Graphics Processing Unit) while maintaining the accuracy of numerical integration at the desired level. For this reason,...
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Jacobi and gauss-seidel preconditioned complex conjugate gradient method with GPU acceleration for finite element method
PublikacjaIn this paper two implementations of iterative solvers for solving complex symmetric and sparse systems resulting from finite element method applied to wave equation are discussed. The problem under investigation is a dielectric resonator antenna (DRA) discretized by FEM with vector elements of the second order (LT/QN). The solvers use the preconditioned conjugate gradient (pcg) method implemented on Graphics Processing Unit (GPU)...
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On tracking properties of real-valued generalized adaptive notch filters
PublikacjaGeneralized adaptive notch filters (GANFs) are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The paper presents results of local performance analysis of a real-valued GANF algorithm, i.e., algorithm designed to track parameters of a real-valued system. This is an extension of the previous work which focused...
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GPU-Accelerated Finite-Element Matrix Generation for Lossless, Lossy, and Tensor Media [EM Programmer's Notebook]
PublikacjaThis 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...
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Generalized adaptive notch smoothers for real-valued signals and systems
PublikacjaSystems with quasi-periodically varying coefficients can be tracked using the algorithms known as generalized adaptive notch filters (GANFs). GANF algorithms can be considered an extension, to the system case, of classical adaptive notch filters (ANFs). We show that estimation accuracy of the existing algorithms, as well as their robustness to the choice of design parameters, can be considerably improved by means of compensating...
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Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations
PublikacjaIn this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.
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Quasi-solutions for generalized second order differential equations with deviating arguments
PublikacjaThis paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.