Related papers: Harmonic Extension for Multiscale Analysis and Mod…
Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal…
We extend a classical approximation result of harmonic functions in planar domains due to Bernstein and Walsch to the setting of harmonic functions in Riemann surfaces. This result gives an exact characterization of the rate at which a…
We develop a mathematically and physically sound definition of the spectrally-hyperviscous Navier-Stokes equations (SHNSE) on general bounded domains \Omega with zero (no-slip) boundary conditions prescribed on \varGamma=\partial\varOmega.…
Convolution quadrature (CQ) methods have enjoyed tremendous interest in recent years as an efficient tool for solving time-domain wave problems in unbounded domains via boundary integral equation techniques. In this paper we consider CQ…
Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its…
Boundary conforming coordinates are commonly used in plasma physics to describe the geometry of toroidal domains, for example, in three-dimensional magnetohydrodynamic equilibrium solvers. The magnetohydrodynamic equilibrium configuration…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for…
Based on the Fourier extension, we propose an oversampling collocation method for solving the elliptic partial differential equations with variable coefficients over arbitrary irregular domains. This method only uses the function values on…
In this work, we initiate the study of the biharmonic heat equation in a spatial bounded domain subject to dynamic boundary conditions involving the bi-Laplace-Beltrami operator on the boundary. The boundary heat equation is coupled to the…
It was shown that an infinite convergent sequence of improving non-increasing upper bounds to the ground state energy of a slow-moving acoustical polaron can be obtained by means of generalized variational method. The proposed approach is…
This paper presents a new approach for solving the close evaluation problem in three dimensions, commonly encountered while solving linear elliptic partial differential equations via potential theory. The goal is to evaluate layer…
A general self-consistency approach allows a thorough treatment of the corrections to the mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on the…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation…
In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…
Approximating solutions of ordinary and partial differential equations constitutes a significant challenge. Based on functional expressions that inherently depend on neural networks, neural forms are specifically designed to precisely…
We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…