Related papers: New stable method to solve heat conduction problem…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG…
Heat conduction is quite common in natural, industrial, and military applications. In this work, the updated Lagrangian particle hydrodynamics (ULPH) theory, is utilized and applied to solve heat conduction problems. Since heat conduction…
In this paper, we establish a H\"older-type quantitative estimate of unique continuation for solutions to the heat equation with Coulomb potentials in either a bounded convex domain or a $C^2$-smooth bounded domain. The approach is based on…
We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…
We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
We present two dimensional numerical simulations of a natural convection problem in an unbounded domain. A thermal stratification is applied in the vertical direction and the flow circulation is induced by a heat island located on the…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
We derive thermodynamically consistent models for diblock copolymer solutions coupled with the electric and magnetic field, respectively. These models satisfy the second law of thermodynamics and therefore are therefore thermodynamically…
In this paper we combine a flexible covariant formulation of the shallow water equations with the semi-implicit numerical scheme developed over the years by Casulli and collaborators. After adopting an orthogonal, but non-orthonormal,…
Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution are finite difference schemes, which can be reduced to the linear algebra problem. We consider…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only bounded. We show that under a Cordes type condition the…
We propose an explicit-implicit scheme for numerically solving Special Relativistic Radiation Hydrodynamic (RRHD) equations, which ensures a conservation of total energy and momentum (matter and radiation). In our scheme, 0th and 1st moment…
In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while…
We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…
We study in this paper the periodic homogenization problem related to a strongly nonlinear reaction-diffusion equation. Owing to the large reaction term, the homogenized equation has a rather quite different form which puts together both…
Combined heat and power dispatch promotes interactions and synergies between electric power systems and district heating systems. However, nonlinear and nonconvex heating flow imposes significant challenges on finding qualified solutions…