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Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) is a popular sharp interface theory. Using matched asymptotic analysis, we show how to quantitatively map the sharp…
We introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins--Sekerka problem. The discretization uses…
We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete…
A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…
Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity…
Accurate predictions of thermo-mechanically coupled process in metals can lead to a reduction of cost and an increase of productivity in manufacturing processes such as forming. For modeling these coupled processes with the finite element…
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…
Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are…
The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and…
We study in this paper the accuracy and stability of partially and fully implicit schemes for phase field modeling. Through theoretical and numerical analysis of Allen-Cahn and Cahn-Hillard models, we investigate the potential problems of…
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Harnessing modern parallel computing resources to achieve complex multi-physics simulations is a daunting task. The Multiphysics Object Oriented Simulation Environment (MOOSE) aims to enable such development by providing simplified…
This paper presents an efficient and quantitative phase-field model for elastically heterogeneous alloys that ensures the two mechanical compatibilities$\unicode{x2014}$static and kinematic, in conjunction with chemical equilibrium within…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
Fluid phase behavior of charge-stabilized colloidal suspensions is explored by applying a new variant of the Gibbs ensemble Monte Carlo simulation method to a coarse-grained one-component model with implicit microions and solvent. The…
This study introduces a hybrid fluid simulation approach that integrates generative diffusion models with physics-based simulations, aiming at reducing the computational costs of flow simulations while still honoring all the physical…