相关论文: ATEQ: Adaptive Toroidal Equilibrium code
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…
The TJ toroidal tearing mode code is used to make realistic predictions of the electron cyclotron emission (ECE) signals generated by neoclassical tearing modes (NTMs) in an ITER-like tokamak plasma equilibrium. In the so-called "outer…
In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the…
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…
Recently, an adaptive variational algorithm termed Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while the number of measurements…
This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross-Pitaevskii and Kohn-Sham equation arising in computational physics and chemistry. These problems characterize critical points of energy…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfv\'en eigenmodes and energetic particle transport in tokamak plasmas. In order…
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global…
Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching…
We introduce a new tensor integration method for time-dependent PDEs that controls the tensor rank of the PDE solution via time-dependent diffeomorphic coordinate transformations. Such coordinate transformations are generated by minimizing…
We address the linear-mode analysis performed near an equilibrium configuration in the fluid rest frame with a dynamical magnetic field perturbed on a constant configuration. We develop a simple and general algorithm for an analytic…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
We consider a coefficient inverse problem for the dielectric permittivity in Maxwell's equations, with data consisting of boundary measurements of one or two backscattered or transmitted waves. The problem is treated using a Lagrangian…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…
Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…