Related papers: Meshless RBF based pseudospectral solution of acou…

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…

We introduce an exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates. This solution, called vector Space-Fractional Bessel Beam (SFBB), has been established from the Lorenz' gauge…

In this article, we present the time-space Chebyshev pseudospectral method (TS-CPsM) to approximate a solution to the generalised Burgers-Fisher (gBF) equation. The Chebyshev-Gauss-Lobatto (CGL) points serve as the foundation for the…

The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…

A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial…

Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems.…

Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined.…

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…

Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…

The stepwise coupled-mode model is a classic approach for solving range-dependent sound propagation problems. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments…

Radial Basis Function-generated Finite Differences (RBF-FD) is a popular variant of local strong-form meshless methods that do not require a predefined connection between the nodes, making it easier to adapt node-distribution to the problem…

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…

Stochastic Barrier Functions (SBFs) certify the safety of stochastic systems by formulating a functional optimization problem, which state-of-the-art methods solve using Sum-of-Squares (SoS) polynomials. This work focuses on polynomial SBFs…

Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…

Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

Partial Differential Equations (PDEs) models for wave propagation in inhomogeneous media are relevant for many applications. We will discuss numerical methods tailored for tackling problems governed by these variable-coefficient PDEs.…

Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain…

This paper proposes a Chebyshev polynomial expansion framework for the recovery of a continuous angular power spectrum (APS) from channel covariance. By exploiting the orthogonality of Chebyshev polynomials in a transformed domain, we…