Related papers: Non-overlapping domain decomposition methods in st…
We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…
In this paper we propose on continuous level a class of domain decomposition methods of Robin-Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
All simulation approaches eventually face limits in computational scalability when applied to large spatiotemporal domains. This challenge becomes especially apparent in molecular-level particle simulations, where high spatial and temporal…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…
We establish a novel approach to probing spatially resolved multi-time correlation functions of interacting many-body systems, with scalable experimental overhead. Specifically, designing nonlinear measurement protocols for multidimensional…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious…
Multifields datasets are common in a large number of research and engineering applications of computational science. The effective visualization of the corresponding datasets can facilitate their analysis by elucidating the complex and…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…
The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing,…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…