Related papers: New stable method to solve heat conduction problem…
We introduce the Closest Point Heat Method (CPHM), a novel approach for solving the surface Eikonal equation on general smooth surfaces. Building on the strengths of the classical heat method, such as simplicity of implementation and…
Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration…
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Two Galerkin methods are applied to a problem of convection with uniform internal heat source are given. With each method analytical results are obtained and discussed. They concern the parameter representing the heating rate. Numerical…
In this paper, we develop a class of robust numerical methods for solving dynamical systems with multiple time scales. We first represent the solution of a multiscale dynamical system as a transformation of a slowly varying solution. Then,…
Existing algorithms with iterations as the principle for 3D inverse heat conduction problems (IHCPs) are usually time-consuming. With the recent advancements in deep learning techniques, it is possible to apply the neural network to compute…
The past decade has witnessed a surge of endeavors in statistical inference for high-dimensional sparse regression, particularly via de-biasing or relaxed orthogonalization. Nevertheless, these techniques typically require a more stringent…
A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time dependent radiation transport equation is obtained using the discrete ordinates method…
We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
This paper presents an implicit solution formula for the Hamilton-Jacobi partial differential equation (HJ PDE). The formula is derived using the method of characteristics and is shown to coincide with the Hopf and Lax formulas in the case…
We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqueness of the exact solution in a neighborhood of a…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
In this paper, we have used the QUICK scheme of the finite volume method to investigate the problem of steady 2-D free convective incompressible flow with heat and mass transfer in an inclined rectangular domain at different Rayleigh…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…
We consider a multilayer hyperbolic-parabolic PDE system which constitutes a coupling of 3D thermal - 2D elastic - 3D elastic dynamics, in which the boundary interface coupling between 3D fluid and 3D structure is realized via a 2D elastic…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…