Related papers: A numerical method for scattering problems with un…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
We describe an efficient Monte Carlo algorithm for a restricted class of scattering problems in radiation transfer. This class includes many astrophysically interesting problems, including the scattering of ultraviolet and visible light by…
An analytical Green's function is developed to study the acoustic scattering by a flat plate with a serrated edge. The scattered pressure is solved using the Wiener-Hopf technique in conjunction with the adjoint technique. It is shown that…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time…
An efficient method is proposed for numerical solutions of nonlinear Schr\"{o}dinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation,…
The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…
We present a domain decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller…
The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…
Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…
Resource allocation problems in many computer systems can be formulated as mathematical optimization problems. However, finding exact solutions to these problems using off-the-shelf solvers in an online setting is often intractable for…
Layered media have been studied extensively both for their importance in imaging technologies and as an example of a hyperbolic PDE with discontinuous coefficients. From the perspective of acoustic imaging, the time limited impulse response…