Related papers: An Implementation of the Finite Element Method in …
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
In the lead up to fault tolerance, the utility of quantum computing will be determined by how adequately the effects of noise can be circumvented in quantum algorithms. Hybrid quantum-classical algorithms such as the variational quantum…
Accurate quantum chemistry simulations remain challenging on classical computers for problems of industrially relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible.…
The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
We study the Landau-de Gennes Q-tensor model of liquid crystals subjected to an electric field and develop a fully discrete numerical scheme for its solution. The scheme uses a convex splitting of the bulk potential, and we introduce a…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…
We outline a proposal to test quantum mechanics in the high-complexity regime using noisy intermediate-scale quantum (NISQ) devices. The procedure involves simulating a non-Clifford random circuit, followed by its inverse, and then checking…
We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
In this paper, we explore (2+1)D quantum electrodynamics (QED) at finite density on a quantum computer, including two fermion flavors. Our method employs an efficient gauge-invariant ansatz together with a quantum circuit structure that…
In many industries, including aerospace and defense, waveform analysis is commonly conducted to compute the resonance of physical objects, with the Finite Element Method (FEM) being the standard approach. The Finite Difference Method (FDM)…
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…
Quantum technologies work by utilizing properties inherent in quantum systems such as quantum coherence and quantum entanglement and are expected to be superior to classical counterparts for solving certain problems in science and…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…