相关论文: A Parametric Interpolation Framework for 1D Scalar…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
We consider DPG methods with optimal test functions and broken test spaces based on ultra-weak formulations of general second order elliptic problems. Under some assumptions on the regularity of solutions of the model problem and its…
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…
This paper investigates the use of $\ell^1$ regularization for solving hyperbolic conservation laws based on high order discontinuous Galerkin (DG) approximations. We first use the polynomial annihilation method to construct a high order…
We present error estimates of the fully semi-Lagrangian scheme with high-order interpolation operators, solving the initial value problems for the one-dimensional nonlinear diffusive conservation laws, including the Burgers equations. We…
A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed guaranteed computation methods for both eigenvalues and…
Parameter-elliptic boundary-value problems are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. The latter are the H\"ormander…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
In the course of this research, we employ the Gauss-Bonnet equation of motion alongside the scalar field and potential to acquire a fresh solution for a spherically symmetrical charged black hole. Specifically, we derive this black hole…
We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-oscillatory (WENO)…
The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying…
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Deep learning methods, which exploit auto-differentiation to compute derivatives without dispersion or dissipation errors, have recently emerged as a compelling alternative to classical mesh-based numerical schemes for solving hyperbolic…
We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is…
We present sufficient conditions on a smooth uniformly flat hypersurface W in the unit ball to be an interpolation hypersurface or a sampling hypersurface for generalized Bergman spaces associated to the unit ball with its Bergman metric.…
We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latter…
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission conditions, and exchange of information between subdomains…