- 标题
- 摘要
- 关键词
- 实验方案
- 产品
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Sparsifying preconditioner for the time-harmonic Maxwell's equations
摘要： This paper presents the sparsifying preconditioner for the time-harmonic Maxwell’s equations in the integral formulation. Following the work on sparsifying preconditioner for the Lippmann–Schwinger equation, this paper generalizes that approach from the scalar wave case to the vector case. The key idea is to construct a sparse approximation to the dense system by minimizing the non-local interactions in the integral equation, which allows for applying sparse linear solvers to reduce the computational cost. When combined with the standard GMRES solver, the number of preconditioned iterations remains small and essentially independent of the frequency. This suggests that, when the sparsifying preconditioner is adopted, solving the dense integral system can be done as efficiently as solving the sparse system from PDE discretization.
关键词： Electromagnetic scattering,Preconditioner,Maxwell’s equations,Sparse linear algebra
更新于2025-09-23 15:23:52
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[IEEE 2019 IEEE High Power Diode Lasers and Systems Conference (HPD) - Coventry, United Kingdom (2019.10.9-2019.10.10)] 2019 IEEE High Power Diode Lasers and Systems Conference (HPD) - Double-asymmetric-structure 1.5 ?? m high power laser diodes
摘要： Matrix inversion is a fundamental operation for solving linear equations for many computational applications, especially for various emerging big data applications. However, it is a challenging task to invert large-scale matrices of extremely high order (several thousands or millions), which are common in most Web-scale systems, such as social networks and recommendation systems. In this paper, we present a lower upper decomposition-based block-recursive algorithm for large-scale matrix inversion. We present its well-designed implementation with optimized data structure, reduction of space complexity, and effective matrix multiplication on the Spark parallel computing platform. The experimental evaluation results show that the proposed algorithm is efficient to invert large-scale matrices on a cluster composed of commodity servers and is scalable for inverting even larger matrices. The proposed algorithm and implementation will become a solid foundation for building a high-performance linear algebra library on Spark for big data processing and applications.
关键词： linear algebra,parallel algorithm,distributed computing,Matrix inversion,LU decomposition,Spark
更新于2025-09-19 17:13:59
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[IEEE 2019 21st European Conference on Power Electronics and Applications (EPE '19 ECCE Europe) - Genova, Italy (2019.9.3-2019.9.5)] 2019 21st European Conference on Power Electronics and Applications (EPE '19 ECCE Europe) - Analysis of an LLC Converter with Planar Inverse Coupled Current Doubler Rectifier using Silicon and GaN devices
摘要： Matrix inversion is a fundamental operation for solving linear equations for many computational applications, especially for various emerging big data applications. However, it is a challenging task to invert large-scale matrices of extremely high order (several thousands or millions), which are common in most Web-scale systems, such as social networks and recommendation systems. In this paper, we present a lower upper decomposition-based block-recursive algorithm for large-scale matrix inversion. We present its well-designed implementation with optimized data structure, reduction of space complexity, and effective matrix multiplication on the Spark parallel computing platform. The experimental evaluation results show that the proposed algorithm is efficient to invert large-scale matrices on a cluster composed of commodity servers and is scalable for inverting even larger matrices. The proposed algorithm and implementation will become a solid foundation for building a high-performance linear algebra library on Spark for big data processing and applications.
关键词： linear algebra,parallel algorithm,distributed computing,Matrix inversion,LU decomposition,Spark
更新于2025-09-19 17:13:59
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[IEEE 2019 IEEE International Electron Devices Meeting (IEDM) - San Francisco, CA, USA (2019.12.7-2019.12.11)] 2019 IEEE International Electron Devices Meeting (IEDM) - First Demonstration of Waveguide-Integrated Black Phosphorus Electro-Optic Modulator for Mid-Infrared Beyond 4 ??m
摘要： Matrix inversion is a fundamental operation for solving linear equations for many computational applications, especially for various emerging big data applications. However, it is a challenging task to invert large-scale matrices of extremely high order (several thousands or millions), which are common in most Web-scale systems, such as social networks and recommendation systems. In this paper, we present a lower upper decomposition-based block-recursive algorithm for large-scale matrix inversion. We present its well-designed implementation with optimized data structure, reduction of space complexity, and effective matrix multiplication on the Spark parallel computing platform. The experimental evaluation results show that the proposed algorithm is efficient to invert large-scale matrices on a cluster composed of commodity servers and is scalable for inverting even larger matrices. The proposed algorithm and implementation will become a solid foundation for building a high-performance linear algebra library on Spark for big data processing and applications.
关键词： linear algebra,parallel algorithm,distributed computing,Matrix inversion,LU decomposition,Spark
更新于2025-09-16 10:30:52