Related papers: Smoothed aggregation algebraic multigrid for probl…
Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…
A multigrid framework is described for multiphysics applications. The framework allows one to construct, adapt, and tailor a monolithic multigrid methodology to different linear systems coming from discretized partial differential…
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…
Using field theoretic renormalization, an MBE-type growth process with an obliquely incident influx of atoms is examined. The projection of the beam on the substrate plane selects a "parallel" direction, with rotational invariance…
Magneto-active elastomers (MAEs) are composite materials comprising an elastomer matrix with embedded magnetic particles, endowing the composite with coupled effective magneto-mechanical responses. It is widely reported that anisotropic…
When a colloid is mixed with a depletant such as a non-adsorbing polymer, one observes attractive effective interactions between the colloidal particles. If these particles are anisotropic, analysis of these effective interactions is…
Randomized smoothing has achieved great success for certified robustness against adversarial perturbations. Given any arbitrary classifier, randomized smoothing can guarantee the classifier's prediction over the perturbed input with…
We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while…
In this paper the relaxed micromorphic material model for anisotropic elasticity is used to describe the dynamical behavior of a band-gap metamaterial with tetragonal symmetry. Unlike other continuum models (Cauchy, Cosserat, second…
Strain-engineering of materials encompasses significant elastic deformation and leads to breaking of the lattice symmetry and as a consequence to the emergence of optical anisotropy. However, the capability to image and map local strain…
Solid state wafers are indispensable components in material science as substrates for epitaxial homo- or hetero-structures or carriers for two-dimensional materials. However, a reliable determination of magnetic properties of nanomaterials…
This paper presents Space-Time MultiGrid (STMG) methods which are suitable for performing topology optimisation of transient heat conduction problems. The proposed methods use a pointwise smoother and uniform Cartesian space-time meshes.…
When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise…
Heavy-ball momentum with decaying learning rates is widely used with SGD for optimizing deep learning models. In contrast to its empirical popularity, the understanding of its theoretical property is still quite limited, especially under…
Quantitative phase field models have been extensively used to study the solidification behavior of alloys under different conditions. However, a longstanding challenge of phase field models is the directional bias caused by the…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
Algorithms for many hypergraph problems, including partitioning, utilize multilevel frameworks to achieve a good trade-off between the performance and the quality of results. In this paper we introduce two novel aggregative coarsening…
We present the Super-Localized Orthogonal Decomposition (SLOD) method for the numerical homogenization of linear elasticity problems with multiscale microstructures modeled by a heterogeneous coefficient field without any periodicity or…