Related papers: A novel iterative time integration scheme for line…
We show that adaptive time stepping in particle accelerator simulation is an enhancement for certain problems. The new algorithm has been implemented in the OPAL (Object Oriented Parallel Accelerator Library) framework, and is compared to…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an…
Phase field models are promising to tackle various fracture problems where a diffusive crack is introduced and modelled using the phase variable. Owing to the non-convexity of the energy functional, the derived partial differential…
We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and…
This paper is devoted to a weak Galerkin (WG) finite element method for linear poroelasticity problems where weakly defined divergence and gradient operators over discontinuous functions are introduced. We establish both the continuous and…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…
In this paper, we consider partitioned numerical methods for quasi-static multiple-network poroelasticity (MPET) equations, generalizations of the Biot model in poroelasticity for multiple pore networks. Two partitioned numerical methods…
Modeling flow in geosystems with natural fault is a challenging problem due to low permeability of fault compared to its surrounding porous media. One way to predict the behavior of the flow while taking the effects of fault into account is…
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
We present a priori error estimates for a multirate time-stepping scheme for coupled differential equations. The discretization is based on Galerkin methods in time using two different time meshes for two parts of the problem. We aim at…
We give explicit criteria of solvability for families of linear systems on time scales. We introduce a new method of embedding a time scale into a non-autonomous system of ODEs. This will be the first step to implementing the structural…