Related papers: A Fourier-Bessel method with a regularization stra…
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition…
We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of…
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary value problems. Its main drawback is that it often leads to ill-conditioned systems of equations. In this paper we investigate for the…
This paper presents regularity results and associated high-order numerical methods for one-dimensional Fractional-Laplacian boundary-value problems. On the basis of a factorization of solutions as a product of a certain edge-singular weight…
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 focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
In the present paper we establish the solvability of the Regularity boundary value problem in domains with (flat and Lipschitz) lower dimensional boundaries for operators whose coefficients exhibit small oscillations analogous to the…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method,…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
The complex Helmholtz equation $(\Delta + k^2)u=f$ (where $k\in{\mathbb R},u(\cdot),f(\cdot)\in{\mathbb C}$) is a mainstay of computational wave simulation. Despite its apparent simplicity, efficient numerical methods are challenging to…
Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion…