共查询到4条相似文献,搜索用时 0 毫秒
1.
This paper presents a fourth-order Cartesian grid based boundary integral
method (BIM) for heterogeneous interface problems in two and three dimensional
space, where the problem interfaces are irregular and can be explicitly given by parametric curves or implicitly defined by level set functions. The method reformulates the
governing equation with interface conditions into boundary integral equations (BIEs)
and reinterprets the involved integrals as solutions to some simple interface problems
in an extended regular region. Solution of the simple equivalent interface problems for
integral evaluation relies on a fourth-order finite difference method with an FFT-based
fast elliptic solver. The structure of the coefficient matrix is preserved even with the
existence of the interface. In the whole calculation process, analytical expressions of
Green’s functions are never determined, formulated or computed. This is the novelty
of the proposed kernel-free boundary integral (KFBI) method. Numerical experiments
in both two and three dimensions are shown to demonstrate the algorithm efficiency
and solution accuracy even for problems with a large diffusion coefficient ratio. 相似文献
2.
A Fourth-Order Upwinding Embedded Boundary Method (UEBM) for Maxwell's Equations in Media with Material Interfaces: Part I 下载免费PDF全文
In this paper, we present a new fourth-order upwinding embedded boundary method (UEBM) over Cartesian grids, originally proposed in the Journal of Computational Physics [190 (2003), pp. 159-183.] as a second-order method for treating material interfaces for Maxwell's equations. In addition to the idea of the UEBM to evolve solutions at interfaces, we utilize the ghost fluid method to construct finite difference approximation of spatial derivatives at Cartesian grid points near the material interfaces. As a result, Runge-Kutta type time discretization can be used for the semidiscretized system to yield an overall fourth-order method, in contrast to the original second-order UEBM based on a Lax-Wendroff type difference. The final scheme allows time step sizes independent of the interface locations. Numerical examples are given to demonstrate the fourth-order accuracy as well as the stability of the method. We tested the scheme for several wave problems with various material interface locations, including electromagnetic scattering of a plane wave incident on a planar boundary and a two-dimensional electromagnetic application with an interface parallel to the y-axis. 相似文献
3.
A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation 下载免费PDF全文
Wei Leng & Lili Ju 《Communications In Computational Physics》2021,29(2):357-395
In this paper, we propose and test a novel diagonal sweeping domain
decomposition method (DDM) with source transfer for solving the high-frequency
Helmholtz equation in$\mathbb{R}^n$. In the method the computational domain is partitioned into
overlapping checkerboard subdomains for source transfer with the perfectly matched
layer (PML) technique, then a set of diagonal sweeps over the subdomains are specially
designed to solve the system efficiently. The method improves the additive overlapping DDM [43] and the L-sweeps method [50] by employing a more efficient subdomain solving order. We show that the method achieves the exact solution of the global
PML problem with $2^n$ sweeps in the constant medium case. Although the sweeping
usually implies sequential subdomain solves, the number of sequential steps required
for each sweep in the method is only proportional to the $n$-th root of the number of
subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus it is very suitable for parallel computing of the Helmholtz problem with
multiple right-hand sides through the pipeline processing. Extensive numerical experiments in two and three dimensions are presented to demonstrate the effectiveness
and efficiency of the proposed method. 相似文献
4.
An Augmented Lagrangian Uzawa Iterative Method for Solving Double Saddle-Point Systems with Semidefinite (2,2) Block and Its Application to DLM/FD Method for Elliptic Interface Problems 下载免费PDF全文
Cheng Wang & Pengtao Sun 《Communications In Computational Physics》2021,30(1):124-143
In this paper, an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite (2,2) block. Convergence of the iterative method is proved under the assumption that the double saddle-point problem exists a unique solution. An application ofthe iterative method to the double saddle-point systems arising from the distributedLagrange multiplier/fictitious domain (DLM/FD) finite element method for solvingelliptic interface problems is also presented, in which the existence and uniquenessof the double saddle-point system is guaranteed by the analysis of the DLM/FD finite element method. Numerical experiments are conducted to validate the theoreticalresults and to study the performance of the proposed iterative method. 相似文献