相关论文: Resolving the Gibbs phenomenon via a discontinuous…
We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of…
Our interest in this paper is a generalization of the additive Deligne-Simpson problem which is originally defined for Fuchsian differential equations on the Riemann sphere. We shall extend this problem to differential equations having an…
Recent developments in the context of minimum residual finite element methods are paving the way for designing finite element methods in non-standard function spaces. This, in particular, permits the selection of a solution space in which…
This work presents a deep learning-based framework for the solution of partial differential equations on complex computational domains described with computer-aided design tools. To account for the underlying distribution of the training…
We consider the presence of oscillations in the primordial bispectrum, inspired by three different cosmological models; features in the primordial potential, resonant type non-Gaussianities and deviation from the standard Bunch Davies…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
Two models were recently proposed to explore the robust hardness of Gr\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for…
The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
It is a challenge to numerically solve nonlinear partial differential equations whose solution involves discontinuity. In the context of numerical simulators for multi-phase flow in porous media, there exists a long-standing issue known as…
Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…
We consider a damped oscillator mode that is resonantly driven and is coupled to an arbitrary target system via the position quadrature operator. For such a composite open quantum system, we develop a numerical method to compute the reduced…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
We solve and characterize the Lagrange multipliers of a reaction-diffusion system in the Gibbs simplex of R^{N+1} by considering strong solutions of a system of parabolic variational inequalities in R^N. Exploring properties of the two…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method.…