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A New Approach to the Solution of Large, Full Matrix Equations: A Two-Dimensional Potential Flow Feasibility Study

机译：一种求解大型全矩阵方程的新方法：二维势流可行性研究

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摘要

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in computer time can be expected for such problems as compared with the time for a direct matrix solution.

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James, R. M.; Clark, R. W.;
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年度 1979
页码 p.1-83
总页数 83
原文格式 PDF
正文语种 eng
中图分类
关键词
Two dimensional flow ; Eigenvectors ; Fast Fourier transformations ; Feasibility analysis ; Airfoils ; Algorithms ; Computer programs ; Integral equations ; Inviscid flow;

机译：二维流动;特征向量;快速傅立叶变换;可行性分析;翼型;算法;计算机程序;积分方程; Inviscid流;

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8. A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study [R] . James, R. M., Clark, R. W. 1979

机译：一种求解大型全矩阵方程的新方法：二维势流可行性研究

A New Approach to the Solution of Large, Full Matrix Equations: A Two-Dimensional Potential Flow Feasibility Study

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