相关论文: A Parametric Interpolation Framework for 1D Scalar…
An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is…
We demonstrate the equivalence of two classes of $D$-invariant polynomial subspaces introduced in [8] and [9], i.e., these two classes of subspaces are different representations of the breadth-one $D$-invariant subspace. Moreover, we solve…
A Block Structure Preserving Model Order Reduction approach is proposed for Integral Equations methods based on the Augmented Electric Field Integral Equation. This approach allows for representing the unknown fields with dedicated…
We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are…
The reduction problem of the chiral field equation on symmetric spaces is studied. It is shown that the symmetric chiral field has infinitely many local conservation laws. A recursive formula for these conservation laws is derived and the…
We give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is…
Let $(X,d,\mu)$ be a metric measure space with a local regular Dirichlet form. We give necessary and sufficient conditions for a parabolic Harnack inequality with global space-time scaling exponent $\beta\ge 2$ to hold. We show that this…
In this paper, we establish a generalized H{\"o}lder's or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabilization of some damped wave-like evolution equations. This…
We study the problem of the existence and regularity of a probability density in an abstract framework based on a "balancing" with approximating absolutely continuous laws. Typically, the absolutely continuous property for the approximating…
The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…
In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational…
We investigate the possibility to localize scalar field configurations as a model for black hole accretion. We analyze and resolve difficulties encountered when localizing scalar fields in General Relativity. We illustrate this ability with…
We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shannon sampling theorem: It characterizes the spatial and…
We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not rely on a strict maximum principle, and builds instead on a…
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of…
We derive necessary and sufficient conditions for all global symmetries of the most general two Higgs doublet model (2HDM) scalar potential entirely in terms of reparametrization independent, i.e. basis invariant, objects. This culminates…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
It is well-known that univariate cubic spline interpolation, if carried out on point sets with fill distance $h$, converges only like ${\cal O}(h^2)$ in $L_2[a,b]$ for functions in $W_2^2[a,b]$ if no additional assumptions are made. But…
We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result \cite{ref:Has07}. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian…
After the observation in 2012 of a new scalar particle closely resembling the Higgs boson of the Standard Model of particle physics, there is a general consensus that there must be Physics Beyond the Standard Model, with present experiments…