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This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties…

We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic…

A Restricted Boltzmann Machine (RBM) is an unsupervised machine-learning bipartite graphical model that jointly learns a probability distribution over data and extracts their relevant statistical features. As such, RBM were recently…

Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…

We explore the mathematical and numerical aspects of reconstructing a potential energy profile of a molecular bond from its rupture time distribution. While reliable reconstruction of gross attributes, such as the height and the width of an…

A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by…

Wood-composite materials are widely used today as they homogenize humidity related directional deformations. Quantification of these deformations as coefficients is important for construction and engineering and topic of current research…

Triply periodic minimal surface (TPMS) structures, a type of lattice structure, have garnered significant attention due to their lightweight nature, controllability, and excellent mechanical properties. Voxel-based modeling is a widely used…

Within density-functional theory, perturbation theory~(PT) is the state-of-the-art formalism for assessing the response to homogeneous electric fields and the associated material properties, e.g., polarizabilities, dielectric constants, and…

The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…

Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…

The task of estimating the fundamental frequency of a monophonic sound recording, also known as pitch tracking, is fundamental to audio processing with multiple applications in speech processing and music information retrieval. To date, the…

Robust visual place recognition (VPR) requires scene representations that are invariant to various environmental challenges such as seasonal changes and variations due to ambient lighting conditions during day and night. Moreover, a…

We address the problem of efficiently compressing video for conferencing-type applications. We build on recent approaches based on image animation, which can achieve good reconstruction quality at very low bitrate by representing face…

We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…

In this paper, we study numerically the linear damped second-order hyperbolic partial differential equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The…

Two primary challenges stand in the way of practical large-scale quantum computation, namely achieving sufficiently low error rate quantum gates and implementing interesting quantum algorithms with a physically reasonable number of qubits.…