Related papers: Parallel Controllability Methods For the Helmholtz…
We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…
Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…
The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number $k$ grows, due to the equation's elliptic yet noncoercive character and the highly…
The oscillatory waves require sufficient degrees of freedom to resolve. That restriction usually applies also to coarse problems for Schwarz methods. The resulting coarse problem is then too large. To address the issue, a new form of…
In this paper, using the approximate particular solutions of Helmholtz equations, we solve the boundary value problems of Helmholtz equations by combining the methods of fundamental solutions (MFS) with the methods of particular solutions…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are…
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
A new idea for iterative solution of the Helmholtz equation is presented. We show that the iteration which we denote WaveHoltz and which filters the solution to the wave equation with harmonic data evolved over one period, corresponds to a…
We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the…
We develop and analyze a new approach for simultaneously computing multiple solutions to the Helmholtz equation for different frequencies and different forcing functions. The new Multi-Frequency WaveHoltz (MFWH) algorithm is an extension of…
In this article, we investigate certain theoretical aspects of the hierarchical controllability problem in one-dimensional wave equations within a moving domain using Stackelberg strategy. The controls are applied along a portion of the…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter to the solution of a related wave equation. The wave…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
This paper is devoted to study exact controllability of two one-dimensional coupled wave equations with first-order coupling terms with coefficients depending on space and time. We give a necessary and sufficient condition for both exact…
Two approaches to solution of the two-dimensional Helmholtz equation with a "wave number" are proposed. The results can be applied both in numerical areas of physics and in the theory of nonlinear equations. The first approach is based on…