共查询到10条相似文献,搜索用时 87 毫秒
1.
Oliver G. Ernst 《Numerische Mathematik》1996,75(2):175-204
Summary. We introduce an algorithm for the efficient numerical solution of exterior boundary value problems for the Helmholtz equation.
The problem is reformulated as an equivalent one on a bounded domain using an exact non-local boundary condition on a circular
artificial boundary. An FFT-based fast Helmholtz solver is then derived for a finite-element discretization on an annular
domain. The exterior problem for domains of general shape are treated using an imbedding or capacitance matrix method. The
imbedding is achieved in such a way that the resulting capacitance matrix has a favorable spectral distribution leading to
mesh independent convergence rates when Krylov subspace methods are used to solve the capacitance matrix equation.
Received May 2, 1995 相似文献
2.
The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The
existence and uniqueness of the solution of the continuous problem is established with the aid of the monotone operator theory.
The main attention is paid to the investigation of the finite element approximation using numerical integration for the computation
of nonlinear boundary integrals. The solvability of the discrete finite element problem is proved and the convergence of the
approximate solutions to the exact one is analysed.
Received April 15, 1996 / Revised version received November 22, 1996 相似文献
3.
Summary. Simple boundary conditions on an artificial boundary are discussed, then an exact boundary condition on the artificial boundary
is obtained. Approximation to this boundary condition with high accuracy is given, and the error estimates are obtained. A
numerical example is presented, and the numerical results are compared with the exact solution.
Received January 27, 1997 / Revised version received May 14, 1999 / Published online February 17, 2000 相似文献
4.
Takuya Tsuchiya 《Numerische Mathematik》1999,84(1):121-141
Summary. Finite element solutions of strongly nonlinear elliptic boundary value problems are considered. In this paper, using the
Kantorovich theorem, we show that, if the Fréchet derivative of the nonlinear operator defined by the boundary value problem
is an isomorphism at an exact solution, then there exists a locally unique finite element solution near the exact solution.
Moreover, several a priori error estimates are obtained.
Received March 2, 1998 / Published online September 7, 1999 相似文献
5.
W. Spann 《Numerische Mathematik》1994,69(1):103-116
Summary.
An abstract error estimate for the approximation of semicoercive variational
inequalities is obtained provided a certain condition holds for the exact
solution. This condition turns out to be necessary as is demonstrated
analytically and numerically. The results are applied to the finite element
approximation of Poisson's equation with Signorini boundary conditions
and to the obstacle problem for the beam with no fixed boundary conditions.
For second order variational inequalities the condition is always satisfied,
whereas for the beam problem the condition holds if the center of forces
belongs to the interior of the convex hull of the contact set. Applying the error
estimate yields optimal order of convergence in terms of the mesh size
.
The numerical convergence rates observed are in good agreement with the
predicted ones.
Received August 16, 1993 /
Revised version received March 21, 1994 相似文献
6.
Summary. In this paper we design high-order local artificial boundary conditions and present error bounds for the finite element approximation
of an incompressible elastic material in an unbounded domain. The finite element approximation is formulated in a bounded
computational domain using a nonlocal approximate artificial boundary condition or a local one. In fact there are a family
of nonlocal approximate artificial boundary conditions with increasing accuracy (and computational cost) and a family of local
ones for a given artificial boundary. Our error bounds indicate how the errors of the finite element approximations depend
on the mesh size, the terms used in the approximate artificial boundary condition and the location of the artificial boundary.
Numerical examples of an incompressible elastic material outside a circle in the plane is presented. Numerical results demonstrate
the performance of our error bounds.
Received August 31, 1998 / Revised version received November 6, 2001 / Published online March 8, 2002 相似文献
7.
C. I. Goldstein 《Numerische Mathematik》1982,38(1):61-82
Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL
2,H
1 andL
, provided that certain relationships hold between the frequency, mesh size and outer radius. 相似文献
8.
The determination of boundary conditions for the Euler equations of gas dynamics in a pipe with partially open pipe ends is considered. The boundary problem is formulated in terms of the exact solution of the Riemann problem and of the St. Venant equation for quasi-steady flow so that a pressure-driven calculation of boundary conditions is defined. The resulting set of equations is solved by a Newton scheme. The proposed algorithm is able to solve for all inflow and outflow situations including choked and supersonic flow.Received: August 7, 2002; revised: November 11, 2002 相似文献
9.
Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference
between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results.
Received April 2, 1996 / Revised version received July 30, 1990 相似文献
10.
Summary. In this paper we consider the numerical simulations of the incompressible materials on an unbounded domain in . A series of artificial boundary conditions at a circular artificial boundary for solving incompressible materials on an
unbounded domain is given. Then the original problem is reduced to a problem on a bounded domain, which be solved numerically
by a mixed finite element method. The numerical example shows that our artificial boundary conditions are very effective.
ReceivedJune 7, 1995 / Revised version received August 19, 1996 相似文献