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First principles approaches have revolutionized our ability in using computers to predict, explore and design materials. A major advantage commonly associated with these approaches is that they are fully parameter free. However, numerically…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure evolution and solidification that have been…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
The present paper aims at applying uncertainty quantification methodologies to process simulations of powder bed fusion of metal. In particular, for a part-scale thermomechanical model of an Inconel 625 super-alloy beam, we study the…
Uncertainty quantification is essential for the reliable deployment of machine learning models to high-stakes application domains. Uncertainty quantification is all the more challenging when training distribution and test distribution are…
Precisely tracking uncertainties is crucial for robots to successfully and safely operate in unstructured and dynamic environments. We present a probabilistic framework to precisely keep track of uncertainties throughout the entire…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
The paper develops a novel design optimization framework and associated computational techniques for staged deployment optimization of complex systems under operational uncertainties. It proposes a local scenario discretization method that…
Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
We study mathematical and computational models for computing the deformation of fiber-reinforced cross-plied laminates due to external forces. This requires an understanding of both micro-structural effects and different sources of…
We determine the speed of a crystallisation (or more generally, a solidification) front as it advances into the uniform liquid phase after the system has been quenched into the crystalline region of the phase diagram. We calculate the front…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…