A New Sparse Matrix Storage Method forAdaptive Solving of Large Systems
نویسنده
چکیده
We present a new method for storing sparse matrices as a block matrix-graph where the blocks are stored via a compact, row-ordered scheme. This combines the exibility of the graph structure with the high eeciency of the compact storage technique. The inner compact pattern also allows identiication of entries, which often leads to advantages with respect to memory and computing time. Using this technique in the PDE toolbox UG yields a exible solver for large systems of reaction-diiusion-transport equations.
منابع مشابه
Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملاستفاده از نمایش پراکنده و همکاری دوربینها برای کاربردهای نظارت بینایی
With the growth of demand for security and safety, video-based surveillance systems have been employed in a large number of rural and urban areas. The problem of such systems lies in the detection of patterns of behaviors in a dataset that do not conform to normal behaviors. Recently, for behavior classification and abnormal behavior detection, the sparse representation approach is used. In thi...
متن کاملA Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems of Nonlinear Equations
Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...
متن کاملCache efficient implementation for block matrix operations
Efficiently manipulating and operating on block matrices can be beneficial in many applications, among others those involving iteratively solving nonlinear systems. These types of problems consist of repeatedly assembling and solving sparse linear systems. In the case of very large systems, without a careful manipulation of the corresponding matrices, solving can become very time consuming. Thi...
متن کاملCAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS
In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...
متن کامل