Related papers: Hybrid preconditioning for iterative diagonalizati…
This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…
Stochastic Galerkin finite element discretizations of partial differential equations with coefficients characterized by arbitrary distributions lead, in general, to fully block dense linear systems. We propose two novel strategies for…
Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
We present the application of simultaneous diagonalization and minimum energy (SDME) high-order finite element modal bases for simulation of transient non-linear elastodynamic problem, including impact cases with neo-hookean hyperelastic…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
The optimization of circuit parameters of variational quantum algorithms such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA) is a key challenge for the practical deployment of near-term…
Predicting effective thermal conductivity by solving a Partial Differential Equation (PDE) defined on a high-resolution Representative Volume Element (RVE) is a computationally intensive task. In this paper, we tackle the task by proposing…
The paper considers grad-div stabilized equal-order finite elements (FE) methods for the linearized Navier-Stokes equations. A block triangular preconditioner for the resulting system of algebraic equations is proposed which is closely…
Full-potential electronic structure calculations for periodic systems retain the Coulomb singularity at the nuclei, which induces cusp behavior of the orbitals near the nuclei while leaving the interstitial region smooth. This multiscale…
Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such…
We propose a matrix-free finite element (FE) homogenization scheme that is considerably more efficient than generic FE implementations. The efficiency of our scheme follows from a preconditioned well-scaled reformulation allowing for the…
This work presents a new methodology for computing ground states of Bose-Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a pre-processing step, a low-dimensional (coarse)…
We suggest a hybrid quantum-classical routine for the NP-hard Electric Vehicle Fleet Charging and Allocation Problem. The original formulation is a Mixed Integer Linear Program with continuous variables and inequality constraints. To…
We develop a quantum filter diagonalization method (QFD) that lies somewhere between the variational quantum eigensolver (VQE) and the phase estimation algorithm (PEA) in terms of required quantum circuit resources and conceptual…
This paper establishes the iteration-complexity of proximal bundle methods for solving hybrid (i.e., a blend of smooth and nonsmooth) weakly convex composite optimization (HWC-CO) problems. This is done in a unified manner by considering a…