High-order FEM domain decomposition models for high-frequency wave propagation in heterogeneous media

Large scale scientific computing models, requiring iterative algebraic solvers, are needed to simulate high-frequency wave propagation because large degrees of freedom are needed to avoid the Helmholtz computer model pollution effects. In this work, we investigate the use of multiple additive Schwarz type domain decomposition (DD) approximations to efficiently simulate two- and three-dimensional high-frequency wave propagation with high-order FEM. We compare our DD based results with those obtained using a standard geometric multigrid approach for up to 1,000 and $300$ wavelength models in two- and three-dimensions, respectively.     

Coupling projection domain decomposition method and Kansa's method in electrostatic problems

This paper present a novel approach for solving electrostatic problems associated with an asymmetrical shielded stripline and shielded coupled-striplines. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method (also, Kansa's method) with projection domain decomposition method. Under this new method, we just need to solve a Steklov-Poincaré interface equation and the original problem is solved by computing a series of independent subproblems. Two real problems are solved by the proposed approach to demonstrate the accuracy and efficiency.     

Total-FETI domain decomposition method for solution of elasto-plastic problems

In this paper we present an algorithm for the parallel solution of the rate-independent elasto-plastic problems with kinematic hardening. We assume the von Mises plastic criterion and the associated plastic flow rule. The time discretization is based on the implicit Euler method. The corresponding one-time-step problem is formulated in the incremental form with respect to the unknown displacement and discretized spatially by the finite element method. We use an ‘external’ algorithm based on a linearization of the elasto-plastic stress–strain relation by the corresponding tangential operator and we parallelize the arising linearized problem by the Total-FETI method. The numerical experiments were carried out using our novel C/C++ library FLLOP (FETI Light Layer On top of PETSc) at HECToR supercomputer located at EPCC, UK.     

Preconditioning of the coarse problem in the method of balanced domain decomposition by constraints

The method of balanced domain decomposition by constraints is an iterative algorithm for numerical solution of partial differential equations which exploits a non-overlapping partition of a domain. As an essential part of each step, restricted problems are solved on every subdomain and a certain coarse grid solution is found. In this paper we present a new strategy of preconditioning of the coarse problem. This is based on the algebraic multilevel preconditioning technique. We present numerical estimates of constants defining the condition numbers of the preconditioned coarse problems for several two- and three-dimensional elliptic equations.     

A direct spectral domain decomposition method for the computation of rotating flows in a T-shape geometry

This paper presents a direct domain decomposition method, coupled with a Chebyshev collocation approximation, for solving the incompressible Navier-Stokes equations in the vorticity-streamfunction formulation. The method is based on the influence matrix technique used to treat the lack of vorticity boundary conditions on no-slip walls as well as to enforce the continuity conditions at the interfaces between adjacent subdomains. The multi-domain approach is proposed in order to extend the use of spectral approximations to non-rectangular geometries and singular solutions. It is applied to the computation of a four domain configuration, corresponding to a forced throughflow in a rotating channel-cavity system which is important in air cooling devices and cannot be modeled by single-domain spectral approximations.     

Accuracy of a domain decomposition method for the recovering of discontinuous heat sources in metal sheet cutting

This paper describes a method for the retrieval of discontinuous heat sources involved in a metal cutting process. Two smoothing techniques were used in the present study in order to smooth noisy sensor data recorded by temperature sensors. The two smoothing techniques are a least squares polynomial fit and a Lagrangian smoothing. These data are then used to recover the heat source. It is found that the least squares polynomial provides over-smoothed results and the Lagrangian smoothing produces phyically acceptable results of the retrieved heat source. Received: 26 February 1999 / Revised version: 5 July 1999     

A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations

We present a new domain decomposition algorithm for the parallel finite element solution of elliptic partial differential equations. As with most parallel domain decomposition methods each processor is assigned one or more subdomains and an iteration is devised which allows the processors to solve their own subproblem(s) concurrently. The novel feature of this algorithm however is that each of these subproblems is defined over the entire domain—although the vast majority of the degrees of freedom for each subproblem are associated with a single subdomain (owned by the corresponding processor). This ensures that a global mechanism is contained within each of the subproblems tackled and so no separate coarse grid solve is required in order to achieve rapid convergence of the overall iteration. Furthermore, by following the paradigm introduced in 15 , it is demonstrated that this domain decomposition solver may be coupled easily with a conventional mesh refinement code, thus allowing the accuracy, reliability and efficiency of mesh adaptivity to be utilized in a well load-balanced manner. Finally, numerical evidence is presented which suggests that this technique has significant potential, both in terms of the rapid convergence properties and the efficiency of the parallel implementation. Copyright © 2001 John Wiley & Sons, Ltd.     

A parallel fully coupled implicit domain decomposition method for numerical simulation of microfluidic mixing in 3D

A parallel fully coupled implicit fluid solver based on a Newton–Krylov–Schwarz algorithm is developed on top of the Portable, Extensible Toolkit for Scientific computation for the simulation of microfluidic mixing described by the three-dimensional unsteady incompressible Navier–Stokes equations. The popularly used fractional step method, originally designed for high Reynolds number flows, requires some modification of the inviscid-type pressure boundary condition in order to reduce the divergence error near the wall. On the other hand, the fully coupled approach works well without any special treatment of the boundary condition for low Reynolds number microchannel flows. A key component of the algorithm is an additive Schwarz preconditioner, which is used to accelerate the convergence of a linear Krylov-type solver for the saddle-point-type Jacobian systems. As a test case, we carefully study a three-dimensional passive serpentine micromixer and report the parallel performance of the algorithm obtained on a parallel machine with more than one hundred processors.     

A domain decomposition technique for finite element based parametric sweep and tolerance analyses of microwave passive devices

A domain decomposition approach is here applied to the finite element solution of a multiport waveguide passive device. The approach allows separating the problem in multiple, coupled subproblems which can be solved individually. By appropriately defining one of these subdomains as containing all the possible variations to be studied it is hence possible to restrict the tolerance analysis to this latter, smaller domain. Numerical results showing the gain in computing time are presented. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations

In this paper, we study the simulation of nonlinear Schrödinger equation in one, two and three dimensions. The proposed method is based on a time-splitting method that decomposes the original problem into two parts, a linear equation and a nonlinear equation. The linear equation in one dimension is approximated with the Chebyshev pseudo-spectral collocation method in space variable and the Crank–Nicolson method in time; while the nonlinear equation with constant coefficients can be solved exactly. As the goal of the present paper is to study the nonlinear Schrödinger equation in the large finite domain, we propose a domain decomposition method. In comparison with the single-domain, the multi-domain methods can produce a sparse differentiation matrix with fewer memory space and less computations. In this study, we choose an overlapping multi-domain scheme. By applying the alternating direction implicit technique, we extend this efficient method to solve the nonlinear Schrödinger equation both in two and three dimensions, while for the solution at each time step, it only needs to solve a sequence of linear partial differential equations in one dimension, respectively. Several examples for one- and multi-dimensional nonlinear Schrödinger equations are presented to demonstrate high accuracy and capability of the proposed method. Some numerical experiments are reported which show that this scheme preserves the conservation laws of charge and energy.     

基于几何均值分解和结构相似度的同源视频时间域复制粘贴篡改快速检测及恢复方法

针对现有方法中篡改检测效率不高、定位不精确的问题,提出了一种基于几何均值分解(GMD)和结构相似度(SSIM)的同源视频复制-粘贴快速篡改检测及恢复的方法。首先,将视频转换为灰度图像序列。其次,将几何均值分解作为检测特征,提出了一个基于块的搜索策略来定位复制序列的起始帧。此外,算法首次将结构相似度用于度量视频两帧之间的相似度,并利用结构相似度对搜索策略得到的起始帧进行复检。由于复制视频序列对应两帧之间的相似度高于未篡改序列对应两帧之间的相似度,提出了一个基于结构相似度的从粗到精的方法来定位复制视频序列的末尾帧。最后,对视频进行恢复。与其他几种经典算法进行对比,实验结果表明,所提方法不仅能够检测经过复制-粘贴篡改操作的视频,而且能准确地定位复制-粘贴序列。此外,该方法在检测精度、召回率和检测时间上有较大提升。     

A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations

In this study, the decomposition method for solving the linear heat equation and nonlinear Burgers equation is implemented with appropriate initial conditions. The application of the method demonstrated that the partial solution in the x-direction requires more computational work when compared with the partial solution developed in the t-direction but the numerical solution in the x-direction are performed extremely well in terms of accuracy and efficiency.