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We present a new divergence-free and well-balanced hybrid FV/FE scheme for the incompressible viscous and resistive MHD equations on unstructured mixed-element meshes in 2 and 3 space dimensions. The equations are split into subsystems. The…
Ferromagnetism (FM) is the cornerstone of permanent magnets, data storage and other technologies that directly impact our everyday life by their implementation in standard applications and devices. When downscaling bulk materials into their…
Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct…
In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the…
Edge plasma turbulence is critical to the performance of magnetic confinement fusion devices. Towards better understanding edge turbulence in both theory and experiment, a custom-built physics-informed deep learning framework constrained by…
An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended…
Low-order virtual element methods (VEM) compute a consistent finite-strain contribution through polynomial projections and rely on stabilization to control the unresolved modes in the projector kernel. In current hyperelastic VEM practice,…
Model-free data-driven computational mechanics (DDCM) is a new paradigm for simulations in solid mechanics. The modeling step associated to the definition of a material constitutive law is circumvented through the introduction of an…
The structural response of masonry arches is strongly dominated by the arch geometry, the stone block dimensions and the interaction with backfill material or surrounding walls. Due to their intrinsic discontinuous nature, the nonlinear…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…
We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett. 109 186404 (2012)] from lattice models to the full chemical Hamiltonian. DMET allows the many-body embedding of arbitrary fragments of a quantum system, even when such…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. In many applications, the spatial distribution of a field needs to be…
Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in…
We present a new set of three-body interaction models based on the Bruch-McGee (BM) potential that are suitable for the study of the energy, structural and elastic properties of solid 4He at high pressure. Our ab initio three-body…