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A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
In this paper, regularity properties, Strichartz type estimates to solutions of multipo{\i}nt Cauchy problem for linear and nonlinear abstract wave equations in vector-valued function spaces are obtained. The equation includes a linear…
We present a novel block-preconditioner for the elastic Helmholtz equation, based on a reduction to acoustic Helmholtz equations. Both versions of the Helmholtz equations are challenging numerically. The elastic Helmholtz equation is…
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…
This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen…
Future radar systems are expected to use waveforms of a high bandwidth, where the main advantage is an improved range resolution. In this paper, a technique to design robust wideband waveforms for a Multiple-Input-Single-Output system is…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
We are interested in numerically solving the Hamilton-Jacobi (HJ) equations, which arise in optimal control and many other applications. Oftentimes, such equations are posed in high dimensions, and this poses great numerical challenges.…
Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for…
In this paper, we study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on real hyperbolic spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an…
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…
Multigrid solvers for hierarchical hybrid grids (HHG) have been proposed to promote the efficient utilization of high performance computer architectures. These HHG meshes are constructed by uniformly refining a relatively coarse fully…
This paper develops and analyzes some interior penalty discontinuous Galerkin methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in the two and three dimensions. It is…
This paper introduces a new pseudodifferential preconditioner for the Helmholtz equation in variable media with absorption. The pseudodifferential operator is associated with the multiplicative inverse to the symbol of the Helmholtz…
We present an efficient matrix-free geometric multigrid method for the elastic Helmholtz equation, and a suitable discretization. Many discretization methods had been considered in the literature for the Helmholtz equations, as well as many…
This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…
Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional…