Related papers: Comparative study of multiscale computational stra…
Over the past decades, discrete dislocation dynamics simulations have been shown to reliably predict the evolution of dislocation microstructures for micrometer-sized metallic samples. Such simulations provide insight into the governing…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty.…
With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…
It is important to accurately model materials' properties at lower length scales (micro-level) while translating the effects to the components and/or system level (macro-level) can significantly reduce the amount of experimentation required…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly…
We study equivalence, in the context of a variable diffusion problem, between (conforming) mixed methods and (primal) nonconforming methods defined on potentially general polytopal partitions. In this first paper of a series of two, we…
Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in a…
Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of…
Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem. The problem is technically ill-posed, and becomes more difficult considering that various sensing…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
We have two basic methods of modeling matter. We can treat matter as a continuum and solve differential equations or we can treat it discretely and solve massive N-body problems. The differential equations produced by meaningful problems…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…