Search results for "System of linear equations"
showing 3 items of 53 documents
Cluster Algorithm Integrated with Modification of Gaussian Elimination to Solve a System of Linear Equations
2020
The data accumulation and their inhomogeneous distribution lead to the issue of large and sparse systems solving in various fields: industrials, emergency management, etc. Complex structure in the data error creates additional risk to obtain an adequate solution. To facilitate problem-solving, we describe the technique that is based on intellectual division of data with following application of cluster algorithm and the modification of Gaussian elimination to different portions of data. In this paper, we present results of developed technique that was applied to samples of synthetic and real data. We compare them with outcomes of other algorithms (intelligence and classical) by using of num…
Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method
2017
For the homogeneous Dirichlet problem involving a system of equations driven by \begin{document}$(p,q)$\end{document} -Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.
A fast Fourier transform based direct solver for the Helmholtz problem
2018
This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is O(N log N) operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed…