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Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach…

Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques. However, when dealing with…

Astrophysical observations suggest that magnetic reconnection in relativistic plasmas plays an important role in the acceleration of energetic particles. Modeling this accurately requires numerical schemes capable of addressing large scales…

Noncollinear (NC) magnetism and spin-orbit coupling (SOC) are indispensable for predictive ab initio materials simulations with pronounced relativistic effects and magnetic frustration, yet they significantly increase the cost of…

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…

It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…

This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…

This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…

Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…

Accurate ab initio modelling of surfaces and interfaces, especially under an applied external potential bias, is important for describing and characterizing various phenomena that occur in electronic, catalytic, and energy storage devices.…

Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…

Optical embedded eigenstates are localized modes of an open structure that are compatible to radiation yet they have infinite lifetime and diverging quality factors. Their realization in nanostructures finite in all dimensions is inherently…

Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of…

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

Multiscale modeling of material properties has emerged as one of the grand challenges in material science and engineering. We provide a comprehensive, though not exhaustive, overview of the current status of multiscale simulations of…

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their…