Related papers: Numerical approximation of multi-phase Penrose-Fif…
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
The saddle-point optimization problems have a lot of practical applications. This paper focuses on such non-smooth problems in decentralized case. This work contains generalization of recently proposed sliding for centralized problem.…
We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays…
We optimize a numerical time-stabilization routine for the phase-field crystal (PFC) models of solidification. By numerical experiments, we showcase that our approach can improve the accuracy of underlying time integration schemes by a few…
A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature…
In this article, we study dynamic chiral symmetry breaking at zero temperature, finite chemical potential and external magnetic field with massless NJL model. We have proposed a mathematical method to classify phases in phase diagram of…
The discretization of Cahn-Hilliard equation with obstacle potential leads to a block 2 by 2 non-linear system, where the p1, 1q block has a non-linear and non-smooth term. Recently a globally convergent Newton Schur method was proposed for…
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element…
A thermodynamically consistent phase-field model is developed to study the non-isothermal grain coalescence during the sintering process, with a potential application to the simulation in unconventional sintering techniques, e.g. spark…
Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the…
Multiphase flow in porous media occurs in several disciplines including petroleum reservoir engineering, petroleum systems' analysis, and CO$_2$ sequestration. While simulations often use a fully implicit discretization to increase the time…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
We consider single-phase flow with solute transport where ions in the fluid can precipitate and form a mineral, and where the mineral can dissolve and release solute into the fluid. Such a setting includes an evolving interface between…
We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion within a phase consisting of multiple species. An approach inspired by augmented Lagrangian…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
We derive an extension of the sequential homotopy method that allows for the application of inexact solvers for the linear (double) saddle-point systems arising in the local semismooth Newton method for the homotopy subproblems. For the…
In this paper we treat the numerical approximation of the two-phase parabolic obstacle-like problem: \[\Delta u -u_t=\lambda^+\cdot\chi_{\{u>0\}}-\lambda^-\cdot\chi_{\{u<0\}},\quad (t,x)\in (0,T)\times\Omega,\] where $T < \infty, \lambda^+…