Related papers: Fast Multipole Preconditioners for Sparse Matrices…
Full-wave 3D electromagnetic simulations of complex planar devices, multilayer interconnects, and chip packages are presented for wide-band frequency-domain analysis using the finite difference integration technique developed in the PETSc…
The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Improvements both on a numerical and computational basis can relief problems related to this bottleneck. This work presents an efficient…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while…
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…
A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach…
Sparse matrices have recently played a significant and impactful role in scientific computing, including artificial intelligence-related fields. According to historical studies on sparse matrix--vector multiplication (SpMV), Krylov subspace…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
A grid-overlay finite difference method is proposed for the numerical approximation of the fractional Laplacian on arbitrary bounded domains. The method uses an unstructured simplicial mesh and an overlay uniform grid for the underlying…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…
We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the…
Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered media…
Cell-free massive multiple-input multiple-output (CF mMIMO) systems serve the user equipments (UEs) by geographically distributed access points (APs) by means of joint transmission and reception. To limit the power consumption due to…
Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…