Related papers: A Parametric Interpolation Framework for 1D Scalar…
A Lax-Oleinik type explicit formula for 1D scalar balance laws has been recently obtained for the pure initial value problem by Adimurthi et al. in [1]. In this article, by introducing a suitable boundary functional, we establish a…
In this paper, we propose two approaches to derive the discrete Poincar\'e inequality for the B-schemes, a family of finite volume discretization schemes, for the one-dimensional Fokker-Planck equation in full space. We study the properties…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
In this paper, we propose and analyze an efficient preconditioning method for the elliptic problem based on the reconstructed discontinuous approximation method. We reconstruct a high-order piecewise polynomial space that arbitrary order…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
This work addresses the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to…
This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
Computing the dispersion relation for two-dimensional photonic crystals is a notoriously challenging task: It involves solving parameterized Helmholtz eigenvalue problems with high-contrast coefficients. To resolve the challenge, we propose…
For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov-Galerkin finite elements. Weighting functions for gradient discretization are parameterized by some…
We address the problem of approximating parametric Fourier imaging problems via interpolation/ extrapolation algorithms that impose smoothing constraints across contiguous values of the parameter. Previous works already proved that…
We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…
In this article, we consider scalar conservation laws with fluxes having spatial discontinuities and possible flat regions and study the following three aspects: (i) existence, (ii) uniqueness and (iii) BV regularity of solutions. We…
A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
In this work we present a framework for enforcing discrete maximum principles in discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to scalar conservation laws as well as hyperbolic systems. Our methodology…
Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an…
For exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carr\'e du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates…
In this paper, we establish space like strong unique continuation property (sucp) for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the…