三维Poisson方程外问题的高阶局部人工边界条件

１引言假设Ｒ３是一分片光滑的闭曲面．是以为边界的无界区域，=Ｒ3是以为边界的有界区域，并且存在球Ｂ0＝ｘｘＲ0我们考虑下面Ｐｏｉｓｓｏｎ方程的外问题：这里f(x），ｇ（x）是，上的已知函数，f(x)的支集是紧的，即存在一个球面=x·x=R1，使得x＝xｘＲ１，有ｆx＝０．令＝，则ｆ（ｘ）的支集包含在中，令＝xx＝，表示u在上的外法向微商．用流量为零的条件代替无限远处条件（３），则我们得到一个新的外问题：我们将分别讨论问题（１）－（３）和（４）－（７）的数值解．由于求解区域的无界性，给数值计算带来了本质性的困难．克服此…

HIGH-ORDER LOCAL ARTIFICIAL BOUNDARY CONDITIONS OF THE EXTERIOR PROBLEM OF POISSON EQUATION IN 3-D SPACE

In this paper the numerical approximation of the exterior problem of Poisson equation in 3-D space is considered. By introducing a spherical artificial boundary the exterior domain is divided into a bounded part and an unbounded part.On the artificial boundary we derived a series of the high-order local artifical boundary conditions. Then we get the reduced approximate boundary value problems defined on the bounded domain. Error analysis between the original problem and the reduced one is obtained. Finally, the numerical example shows the effectiveness of the given method.