Hill, P. A.Parker, J. T.Dickinson, D.Dudson, B. D....
15页
查看更多>>摘要：Tridiagonal matrix inversion is an important operation with many applications. It arises frequently in solving discretized one-dimensional elliptic partial differential equations, and forms the basis for many algorithms for block tridiagonal matrix inversion for discretized PDEs in higher-dimensions. In such systems, this operation is often the scaling bottleneck in parallel computation. In this paper, we derive a hybrid multigridThomas algorithm designed to efficiently invert tridiagonal matrix equations in a highly-scalable fashion in the context of time evolving partial differential equation systems. We decompose the domain between processors, using multigrid to solve on a grid consisting of the boundary points of each processor's local domain. We then reconstruct the solution on each processor using a direct solve with the Thomas algorithm. This algorithm has the same theoretical optimal scaling as cyclic reduction and recursive doubling. We use our algorithm to solve Poisson's equation as part of the spatial discretization of a time-evolving PDE system. Our algorithm is faster than cyclic reduction per inversion and retains good scaling efficiency to twice as many cores. Crown Copyright (c) 2021 Published by Elsevier B.V. All rights reserved.
Zaman, SakhiSiraj-ul-IslamKhan, Muhammad MunibAhmad, Imtiaz...
14页
查看更多>>摘要：Accurate algorithms are proposed for approximation of integrals involving highly oscillatory Bessel function of the first kind over finite and infinite domains. Accordingly, Bessel oscillatory integrals having high oscillatory behavior are transformed into oscillatory integrals with Fourier kernel by using complex line integration technique. The transformed integrals contain an inner non-oscillatory improper integral and an outer highly oscillatory integral. A modified meshfree collocation method with Levin approach is considered to evaluate the transformed oscillatory type integrals numerically. The inner improper complex integrals are evaluated by either Gauss-Laguerre or multi-resolution quadrature. Inherited singularity of the meshfree collocation method at x = 0 is treated by a splitting technique. Error estimates of the proposed algorithms are derived theoretically in the inverse powers of omega and verified numerically. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we introduce a hybrid absorbing boundary condition (HABC) by combining perfectly matched layer (PML) and complete radiation boundary condition (CRBC) for solving a one-dimensional diffraction grating problem. The new boundary condition is devised in such a way that it can enjoy relative advantages from both methods. The well-posedness of the problem with HABC and the convergence of approximate solutions will be analyzed. Numerical examples to illustrate the efficiency of HABC are also presented. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The Henon equation, a generalized form of the Emden equation, admits symmetry breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We discuss a numerical verification method for proving the existence of solutions of the Henon equation on a bounded domain. By applying the method to a line-segment domain and a square domain, we numerically prove the existence of solutions of the Henon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of undiscovered solutions with three peaks on the square domain. (C) 2021 The Authors. Published by Elsevier B.V.
查看更多>>摘要：This paper deals with development and analysis of a finite volume (FV) method for the coupled system describing immiscible compressible two-phase flow, such as water-gas, in porous media, capillary and gravity effects being taken into account. We investigate a fully coupled fully implicit cell-centered "phase-by-phase'' FV scheme for the discretization of such system. The main goal is to incorporate some of the most recent improvements in the scheme and the convergence of the numerical approximation to the weak solution of such models. The spatial discretization uses a TPFA scheme and a new strategy for handling the upwinding. Based on a priori estimates and compactness arguments, we prove the convergence of the numerical approximation to the weak solution. The particular feature in this convergence analysis of the classical engineering scheme based on the "phase-by-phase'' upwinding on an orthogonal mesh relies on the global pressure-saturation fractional flow formulation as was defined relatively recently for immiscible compressible flow in porous media. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu(X). Two numerical experiments are presented to demonstrate the efficiency of this scheme. The first test addresses the evolution in 2D of gas migration through engineered and geological barriers for a deep repository for radioactive waste. The second test case is chosen to test the ability of the method to approximate solutions for 3D problems modeling scenarios of CO2 injection in a fully water-saturated domain. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we study the finite-time ruin problems in the spectrally negative Levy risk models. Suppose that the surplus process of an insurance company is observed periodically in a finite-time interval, and ruin is declared as soon as the observed surplus level is negative. A finite-time Gerber-Shiu expected discounted penalty function is studied. After approximating the common density function of the successive increments of the observed surplus process by frame duality projection, we propose a recursive method for computing the finite-time Gerber-Shiu function. Error analysis is made for the proposed algorithm, and numerical examples are also illustrated to show accuracy and efficiency of our method. (C) 2021 Elsevier B.V. All rights reserved.
Mardanov, Misir J.Melikov, Telman K.Malik, Samin T.
11页
查看更多>>摘要：In the paper, we proposed an approach for studying strong and weak extremums in non-smooth vector problems of calculus of variation, namely, in classic variational problems with fixed ends and with a free right end, and also in a variational problem with higher derivatives. The essence of the proposed approach is to introduce a Weierstrass type variation characterized by a numerical parameter. Necessary conditions for minimum containing as corollaries the Weierstrass condition, its local modification and also the Legendre and transversality conditions are obtained. In the case when the Legendre condition degenerates, equality and inequality type necessary conditions are obtained for the weak local minimum. The examples showing the content-richness of the obtained main results are given. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Convection enhanced drug delivery (CED) is a technique used to make therapeutic agents reach, through a catheter, sites of difficult access. The name of this technique comes from the convective flow originated by a pressure gradient induced at the tip of the catheter. This flow enhances passive diffusion and allows a more efficient spread of the agents by the target site. CED is particularly useful in the treatment of diseases that affect the central nervous system, where the blood-brain barrier prevents the diffusion of most therapeutic agents from the cerebral blood vessels to the brain interstitial space. In this work we deal with the numerical analysis of a coupled system of partial differential equations that can be used to simulate CED in an elastic medium like brain tissue. The model variables are the fluid velocity, the pressure, the tissue deformation, and the agents concentration. We prove the stability of the coupled problem and from the numerical point of view we propose a fully discrete piecewise linear finite element method (FEM). The convergence analysis shows that the method has second order convergence for the pressure, displacement, and concentration. Numerical experiments illustrating the theoretical convergence rates and the behavior of the system are also given. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Method of optimizing the distance between individual elements in the antenna array is presented. Based on the verification of the analytical model for one defined rectangular patch antenna and subsequently for the antenna array, the sweep analysis was per-formed for variant voltage and phase values on each element of the array. The results were used as the input parameters for creating a surrogate model using a neural network for implementation in a micro-controller and use for voltage control in the array. The methodology is illustrated with a typical example. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We propose and analyze a high order unfitted hybridizable discontinuous Galerkin method to numerically solve Oseen equations in a domain Omega having a curved boundary. The domain is approximated by a polyhedral computational domain not necessarily fitting Omega. The boundary condition is transferred to the computational domain through line integrals over the approximation of the gradient of the velocity and a suitable decomposition of the pressure in the computational domain is employed to obtain an approximation of the pressure having zero-mean in the domain Omega. Under assumptions related to the distance between the computational boundary and Omega, we provide stability estimates of the solution that will lead us to the well-posedness of the scheme and also to the error estimates. In particular, we prove that the approximations of the pressure, velocity and its gradient are of order h(k+1), where h is the meshsize and k the polynomial degree of the local discrete spaces. We provide numerical experiments validating the theory and also showing the performance of the method when applied to the steady-state incompressible Navier-Stokes equations. (C) 2021 Elsevier B.V. All rights reserved.
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