Related papers: Reduced Order Modeling based Inexact FETI-DP solve…
Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for…
Lattice-skin structures composed of a thin-shell skin and a lattice infill are widespread in nature and large-scale engineering due to their efficiency and exceptional mechanical properties. Recent advances in additive manufacturing, or 3D…
We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
While linear FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) is an efficient iterative domain decomposition solver for discretized linear PDEs (partial differential equations), nonlinear FETI-DP is its consequent…
This paper introduces a heuristic topology optimization framework for thin-walled, 2D extruded lattice structures subject to complex high-speed loading. The proposed framework optimizes the wall thickness distribution in the lattice cross…
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…
Computational fluid dynamics (CFD) requires a vast amount of compute cycles on contemporary large-scale parallel computers. Hence, performance optimization is a pivotal activity in this field of computational science. Not only does it…
This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of…
In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit…
The capabilities of additive manufacturing have facilitated the design and production of mechanical metamaterials with diverse unit cell geometries. Establishing linkages between the vast design space of unit cells and their effective…
A fast and reliable geometry optimization algorithm is presented that optimizes atomic positions and lattice vectors simultaneously. Using a series of benchmarks, it is shown that the method presented in this paper outperforms in most cases…
We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a…
High-performance computing systems are more and more often based on accelerators. Computing applications targeting those systems often follow a host-driven approach in which hosts offload almost all compute-intensive sections of the code…
BDDC and FETI-DP algorithms are developed for three-dimensional elliptic problems with adaptively enriched coarse components. It is known that these enriched components are necessary in the development of robust preconditioners. To form the…
The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp.~1235--1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp.~128--149] for solving incompressible Stokes equations, are extended to…
Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…