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We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
In this paper we propose on continuous level a class of domain decomposition methods of Robin-Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract…
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the…
In the present work, we study and analyze an efficient iterative coupling method for a dimensionally heterogeneous problem . We consider the case of 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
A new scheme that tightly couples kinetic turbulence codes across a spatial interface is introduced. This scheme evolves from considerations of competing strategies and down-selection. It is found that the use of a composite kinetic…
In this paper, we prove a threshold result for the Robin problem of semilinear parabolic equations
In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The…
We developed a sharp interface level-set approach for two-phase immiscible flow with moving contact lines. The Cox-Voinov model is used to describe the moving contact line. A piecewise linear interface method is used to construct the signed…
This paper considers a family of second-order parabolic equations in divergence form with rapidly oscillating and time-dependent periodic coefficients and an interface between two periodic structures. Following a framework initiated by…
Assessing IC manufacturing process fluctuations and their impacts on IC interconnect performance has become unavoidable for modern DSM designs. However, the construction of parametric interconnect models is often hampered by the rapid…
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3,…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
As has been shown in our previous work, the parallel-in-time direct inverse (ParaDIn) method introduced by Yamaleev and Paudel in (arXiv: 2406.00878v1, 2024) imposes some constraint on the maximum number of time levels, $N_t$, that can be…
This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential…
In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward…