Related papers: Quantum Element Method for Simulation of Quantum E…
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…
We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the…
Quantum error mitigation (EM) is a family of hybrid quantum-classical methods for eliminating or reducing the effect of noise and decoherence on quantum algorithms run on quantum hardware, without applying quantum error correction (EC).…
The so-called matrix-element method (MEM) has long been used successfully as a classification tool in particle physics searches. In the presence of invisible final state particles, the traditional MEM typically assigns probabilities to an…
POD--Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam…
An efficient finite element method (FEM) for calculating eigenvalues and eigenfunctions of quantum billiard systems is presented. We consider the FEM based on triangular $C_1$ continuity quartic interpolation. Various shapes of quantum…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…
We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic…
We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain…