Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAn Efficient Iterative Method for Solving Multiple Scattering in Locally Inhomogeneous Media
88
0
0.0
(
0
)
Added by
Bo Wang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then apply purely outgoing wave decomposition for the scattering field outside the enclosed region. As a result, the original multiple scattering problem can be decomposed into a finite number of single scattering problems, where each of them communicates with the other scattering problems only through its surrounding artificial boundary. Accordingly, they can be solved in a parallel manner at each iteration. This framework enjoys a great flexibility in using different combinations of iterative algorithms and single scattering problem solvers. The spectral element method seamlessly integrated with the non-reflecting boundary condition and the GMRES iteration is advocated and implemented in this work. The convergence of the proposed method is proved by using the compactness of involved integral operators. Ample numerical examples are presented to show its high accuracy and efficiency.
rate research
Read More
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [19] and extends those methods into a more general and unified framework. The main idea of the framework is to reformulate the underlying problem into another problem with a parameter-independent diffusion coefficient and a parameter-dependent (and solution-dependent) right-hand side, a fixed-point iteration is then employed to compute the solution of the reformulated problem. The main benefit of the proposed approach is that an efficient direct solver and a block Krylov subspace iterative solver can be used at each iteration, allowing to reuse the $LU$ matrix factorization or to do an efficient matrix-matrix multiplication for all parameters, which in turn results in significant computation saving. Convergence and rates of convergence are established for the iterative method both at the variational continuous level and at the finite element discrete level under some structure conditions. Several strategies for establishing reformulations of parameter-dependent and random diffusion problems are proposed and their computational complexity is analyzed. Several 1-D and 2-D numerical experiments are also provided to demonstrate the efficiency of the proposed iterative method and to validate the theoretical convergence results.
This paper introduces and analyzes a preconditioned modified of the Hermitian and skew-Hermitian splitting (PMHSS). The large sparse continuous Sylvester equations are solved by PMHSS iterative algorithm based on nonHermitian, complex, positive definite/semidefinite, and symmetric matrices. We prove that the PMHSS is converged under suitable conditions. In addition, we propose an accelerated PMHSS method consisting of two preconditioned matrices and two iteration parameters {alpha}, b{eta}. Theoretical analysis showed that the convergence speed of the accelerated PMHSS is faster compared to the PMHSS. Also, the robustness and efficiency of the proposed two iterative algorithms were demonstrated in numerical experiments.
In this work we consider the transport of a surfactant in a variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three linearization techniques are discussed: the Newton method, the modified Picard and the L-scheme. Based on these, monolithic and splitting schemes are proposed and their convergence is analyzed. The performance of these schemes is illustrated on four numerical examples. For these examples, the number of iterations and the condition numbers of the linear systems emerging in each iteration are presented.
This text proposes a fast, rapidly convergent Nystr{o}m method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while allowing the material properties to jump across the interface. The method works with overlapping coordinate charts as a description of the given scatterer. In particular, it employs partitions of unity to simplify the implementation of high-order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations. To deal with the discontinuous material interface in a high-order manner, a specialized quadrature is used in the boundary region. The approach further utilizes an FFT based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of $O(N log N)$ for an $N$-point discretization. A detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance in terms of both speed and accuracy are presented in this paper.
This paper proposes a novel method to establish the wellposedness and convergence theory of the uniaxial-perfectly-matched-layer (UPML) method in solving a two-dimensional acoustic scattering problem due to a compactly supported source, where the medium consists of two layers separated by the horizontal axis. When perfectly matched layer (PML) is used to truncate the vertical variable only, the medium structure becomes a closed waveguide. The Green function due to a primary source point in this waveguide can be constructed explicitly based on variable separations and Fourier transformations. In the horizontal direction, by properly placing periodical PMLs and locating periodic source points imaged by the primary source point, the exciting waveguide Green functions by those imaging points can be assembled to construct the Green function due to the primary source point for the two-layer medium truncated by a UPML. Incorporated with Greens identities, this UPML Green function directly leads to the wellposedness of the acoustic scattering problem in a UPML truncation with no constraints about wavenumbers or UPML absorbing strength. Consequently, we firstly prove that such a UPML truncating problem is unconditionally resonance free. Moreover, we show, under quite general conditions, that this UPML Green function converges to the exact layered Green function exponentially fast as absorbing strength of the UPML increases, which in turn gives rise to the exponential convergence of the solution of the UPML problem towards the original solution.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
