Related papers: New stable method to solve heat conduction problem…
The effective and efficient numerical solution of Riemann-Hilbert problems has been demonstrated in recent work. With the aid of ideas from the method of nonlinear steepest descent for Riemann-Hilbert problems, the resulting numerical…
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
In the present paper a detailed mathematical model is derived for district heating networks. After semidiscretization of the convective heat equation and introducing coupling conditions at the nodes of the network one gets a…
In this paper, we study how the D-iteration algorithm can be applied to numerically solve the differential equations such as heat equation in 2D or 3D. The method can be applied on the class of problems that can be addressed by the…
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…
In this paper, we consider a semi-classical version of the nonhomogeneous heat equation with singular time-dependent coefficients on the lattice $\hbar \mathbb{Z}^n$. We establish the well-posedeness of such Cauchy equations in the…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
A new parallel-in-time iterative method is proposed for solving the homogeneous second-order wave equation. The new method involves a coarse scale propagator, allowing for larger time steps, and a fine scale propagator which fully resolves…
A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
We present an analysis on the convergence properties of the so-called geometric heat flow equation for computing geodesics (extremal curves) on Riemannian manifolds. Computing geodesics numerically in real time has become an important…
We consider a stochastic heat equation with nonlinear finite-rank space-coloured multiplicative noise that admits a unique nonnegative solution when given nonnegative initial data. Inspired by existing results for fully discrete finite…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with…
Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…