Analytical integrations for the approximation of 3D hyperbolic scalar boundary integral equations

A. Salvadori; A. Temponi

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Analytical integrations for the approximation of 3D hyperbolic scalar boundary integral equations

机译：逼近3D双曲标量边界积分方程的解析积分

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摘要

The present note deals with 3D hyperbolic scalar problems modeled by integral equations [1]. It aims at showing analytical integrations for collocation in time [2] as well as "variational" [3] approximation schemes. Numerical solution is achieved adopting polynomial shape functions of arbitrary degree (in space and time) on a trapezoidal flat tiling of a polygonal domain. Analytical integrations are performed both in space and time for Lebesgue integrals, working in a local coordinate system. For singular integrals, both a limit to the boundary as well as the finite part of Hadamard approach have been pursued. Outcomes and computational issues are presented. Extension to elastodynamics will be the subject of forthcoming publications.

机译：本说明处理由积分方程[1]建模的3D双曲标量问题。它旨在显示时间[2]和“变异” [3]近似方案的并置分析积分。在多边形域的梯形平铺上采用任意程度（在空间和时间上）的多项式形状函数来实现数值解。 Lebesgue积分在空间和时间上都进行了分析积分，并在局部坐标系中进行。对于奇异积分，既寻求边界的限制，也寻求Hadamard方法的有限部分。提出了结果和计算问题。弹性动力学的扩展将是即将出版的主题。

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来源
《Engineering analysis with boundary elements》 |2010年第11期|P.977-994|共18页
作者
A. Salvadori; A. Temponi;
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作者单位

CeSiA - Centra di studio e ricerca di sismologia applicata e dinamica strutturale, DICATA - Dipartimento di lngegneria Civile, Architettura, Territorio e Ambiente, Universita di Brescia, via Bronze 43, 25123 Brescia, Italy;

rnCeSiA - Centra di studio e ricerca di sismologia applicata e dinamica strutturale, DICATA - Dipartimento di lngegneria Civile, Architettura, Territorio e Ambiente, Universita di Brescia, via Bronze 43, 25123 Brescia, Italy;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
scalar wave problem; boundary integral equations; analytical integrations; computational complexity;

机译：标量波问题边界积分方程分析整合;计算复杂度;

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1. Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D [J] . Zapletal Jan, Bouchala Ji?í Applications of mathematics . 2014,第5期

机译：3D Helmholtz方程的超奇异Galerkin边界积分方程的有效半解析积分
2. EFFECTIVE SEMI-ANALYTIC INTEGRATION FOR HYPERSINGULAR GALERKIN BOUNDARY INTEGRAL EQUATIONS FOR THE HELMHOLTZ EQUATION IN 3D [J] . Jan Zapletal, Jiri Bouchala Applications of Mathematics . 2014,第5期

机译：3D Helmholtz方程的超奇异Galerkin边界积分方程的有效半解析积分
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4. A discretization framework for scalar integral equations using the generalized method of moments and locally smooth surface approximations [C] . Nair N. V., Shanker B., Kempel L. 2011 IEEE International Symposium on Antennas and Propagation (APSURSI) . 2011

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5. First passage times: Integral equations, randomization and analytical approximations. [D] . Valov, Angel Veskov. 2009

机译：第一次通过时间：积分方程，随机化和解析近似。
6. Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding [O] . Amelia B. Kreienkamp, Lucy Y. Liu, Mona S. Minkara, -1

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7. Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D [O] . Zapletal, Jan, Bouchala, Jiří 2014

机译：3D Helmholtz方程的超奇异Galerkin边界积分方程的有效半解析积分
8. Initial-Boundary Value Problems for Hyperbolic Equations and Their Difference Approximation with Characteristic Boundary [R] . Michelson, D. 1980

机译：双曲型方程的初边值问题及其特征边界差分逼近

Analytical integrations for the approximation of 3D hyperbolic scalar boundary integral equations

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