Numerical solution of problems on unbounded domains. a review

TL;DR: In this paper, the specification of conditions on artificial boundaries of the computational domain in the simulation of subsonic viscous gas flows is considered, and the steps in the construction and implementation of nonreflecting boundary conditions on the path from one-dimensional linearized Euler equations to real-life problems are described.

Abstract: Transparent boundary conditions for polygonal two-dimensional domains based on the pole condition approach are presented. The discretization of the exterior is done by innite trapezoids, which allows to dene a generalized distance variable. Taking the Laplace transform of the solution w.r.t the distance variable, incoming and outgoing solutions can be distinguished by the location of the singularities. Using special ansatz and test functions, the condition on the location of the singularities yields a new algorithmic realization of transparent boundary conditions.

TL;DR: An efficient method of almost linear complexity is developed for the solution of this system based on the existing recursive algorithm and it is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times.

TL;DR: In this paper, the Perfectly Matching Layer and Infinite Element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain is presented, where traditional hexahedral finite elements are used to model wave propagation in the inner domain and infinite element test functions are implemented in the exterior domain.

TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.

TL;DR: Numerical experiments and numerical comparisons show that the PML technique works better than the others in all cases; using it allows to obtain a higher accuracy in some problems and a release of computational requirements in some others.

TL;DR: In this paper, a new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains.