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A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Microstructural pattern formation, such as dendrite growth, occurs widely in materials and energy systems, significantly influencing material properties and functional performance. While the phase-field method has emerged as a powerful…
With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical…
We present and analyze a new space-time parallel multigrid method for parabolic equations. The method is based on arbitrarily high order discontinuous Galerkin discretizations in time, and a finite element discretization in space. The key…
Shape memory alloys (SMAs) exhibit hysteresis behaviors upon stress and temperature induced loadings. In this contribution, we focus on numerical simulations of microstructure evolution of cubic-to-tetragonal martensitic phase…
In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…
We develop multipoint stress mixed finite element methods for linear elasticity with weak stress symmetry on cuboid grids, which can be reduced to a symmetric and positive definite cell-centered system. The methods employ the lowest-order…
We demonstrate that scalable neuromorphic hardware can implement the finite element method, which is a critical numerical method for engineering and scientific discovery. Our approach maps the sparse interactions between neighboring finite…
This contributions discusses the simulation of magnetothermal effects in superconducting magnets as used in particle accelerators. An iterative coupling scheme using reduced order models between a magnetothermal partial differential model…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
Accelerating materials development requires quantitative linkages between processing, microstructure, and properties. In this work, we introduce a framework for mapping microstructure onto a low-dimensional material manifold that is…
Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…
Needle-like twins are observed experimentally within the transition layer at the martensite-twinned martensite interface. We utilize a phase-field approach to investigate this microstructure. Our goal is to simulate the morphology of the…
Having in mind the modelling of marble degradation under chemical pollutants, e.g.~the sulfation process, we consider governing nonlinear diffusion equations and their numerical approximation.The space domain of a computation is the…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps…