A Direct Implementation of a Modified Boundary Integral Formulation for the Extended Fisher-Kolmogorov Equation

This study is concerned with the numerical approximation of the extended Fisher-Kolmogorov equation with a modified boundary integral method. A key aspect of this formulation is that it relaxes the domain-driven approach of a typical boundary element (BEM) technique. While its discretization keeps faith with the second order accurate BEM formulation, its implementation is element-based. This leads to a local solution of all integral equation and their final assembly into a slender and banded coefficient matrix which is far easier to manipulate numerically. This outcome is much better than working with BEM’s fully populated coefficient matrices resulting from a numerical encounter with the problem domain especially for nonlinear, transient, and heterogeneous problems. Faithful results of high accuracy are achieved when the results obtained herein are compared with those available in literature.

Approximate Formulation and Numerical Solution for Hypersingular Boundary Integral Equations in Plane Elasticity

Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations.

Entropy Formulation for Triply Nonlinear Degenerate Elliptic-Parabolic-Hyperbolic Equation with Zero-Flux Boundary Condition

In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.

A COMPLETE BOUNDARY INTEGRAL FORMULATION FOR STEADY COMPRESSIBLE INVISCID FLOWS GOVERNED BY NONLINEAR EQUATIONS

A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.

耦合边界元法和等效源法的稳健CHIEF法

针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接替换计算常规边界元法中的奇异系数矩阵,进而提出一种具有全频域唯一解、高计算精度和高稳定性的耦合CHIEF法。该方法将等效源方程作为补充方程,不仅解决了传统CHIEF法内点补充方程失效的问题,而且矩阵的间接替换计算避免了直接计算奇异积分,显著提高了计算效率和精度。通过声辐射和声散射的典型算例对比了所提方法、常规边界元法、常规Burton-Miller法和等效源法的计算效果。结果表明,所提方法不仅在全波数域内均能获得唯一解,且其计算精度和效率均优于常规边界元法和常规Burton-Miller方法,其系数矩阵条件数远低于等效源法。

三维电磁固体平片裂纹反对称问题的解法

根据三维无限大横观各向同性电磁固体中位于各向同性面内的任意形状平片裂纹的广义不连续位移边界积分方程和相应的弹性体的边界积分方程的相似性,给出反对称载荷作用下电磁固体边界积分方程的一种解法,其中广义不连续位移包括不连续位移、不连续电势和不连续磁势。通过广义不连续位移建立两类问题广义应力强度因子的关系。作为应用,给出受径向点力作用的圆盘裂纹的应力强度因子。

四边形常数单元离散下的声学非奇异BIE

奇异积分是基于Burton-Miller方程的声学边界元法实现过程的难点之一。关于三角形单元离散的积分单元的已经比较成熟,研究四边形常数单元离散下的声学边界积分方程(BIE),通过构造围绕配点的极小半球面进行积分,求得积分中的发散项,推导四边形常数单元离散下边界积分方程及其法向求导的非奇异表达式,从而得到非奇异Burton-Miller方程。运用Gauss Legendre积分公式计算BIE的S(x)的数值解,对比解析解的计算结果,得出了数值解、解析解以及二者的绝对误差、相对误差随ka的变化规律。实际应用时,当给定精度和ka的值后,可以通过改变所需要的截断项数,使得误差满足给定的精度要求。