Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation
DOI10.1016/j.jcp.2021.110165OpenAlexW3138904207MaRDI QIDQ2131058
Thomas P. Wihler, Benjamin Stamm, Pascal Heid
Publication date: 25 April 2022
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1906.06954
energy minimizationadaptive finite element methodsgradient flowssemilinear elliptic operatorsiterative Galerkin procedureslinear and nonlinear eigenvalue problems
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)
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- GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions
- Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates
- A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations
- Efficiently computing vortex lattices in rapid rotating Bose-Einstein condensates
- Numerical analysis of nonlinear eigenvalue problems
- Convergence of an adaptive Kačanov FEM for quasi-linear problems
- Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems
- Iterative Galerkin discretizations for strongly monotone problems
- Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates
- A posteriori analysis of iterative algorithms for a nonlinear problem
- Energy minimization related to the nonlinear Schrödinger equation
- A minimisation approach for computing the ground state of Gross-Pitaevskii systems
- Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods
- Ground-state solution of Bose--Einstein condensate by directly minimizing the energy functional
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
- Adaptive energy minimisation for \(hp\)-finite element methods
- On the convergence of adaptive iterative linearized Galerkin methods
- An adaptive Newton-method based on a dynamical systems approach
- Two-grid discretization schemes for nonlinear Schrödinger equations
- Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates
- MINIMIZING THE GROSS-PITAEVSKII ENERGY FUNCTIONAL WITH THE SOBOLEV GRADIENT — ANALYTICAL AND NUMERICAL RESULTS
- Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs
- The Finite Element Method: Theory, Implementation, and Applications
- An Inverse Iteration Method for Eigenvalue Problems with Eigenvector Nonlinearities
- A New Sobolev Gradient Method for Direct Minimization of the Gross–Pitaevskii Energy with Rotation
- A Generalized-Laguerre–Fourier–Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose–Einstein Condensates
- An $hp$-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems
- Two-grid methods for a class of nonlinear elliptic eigenvalue problems
- Computation of Ground States of the Gross--Pitaevskii Functional via Riemannian Optimization
- A posteriorierror estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part II: Eigenvalue problems
- Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
- An analysis of finite-dimensional approximations for the ground state solution of Bose–Einstein condensates
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Regularity and hp discontinuous Galerkin finite element approximation of linear elliptic eigenvalue problems with singular potentials
- Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency
- Adaptive iterative linearization Galerkin methods for nonlinear problems
- An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates
- Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations
- A Multigrid Method for Ground State Solution of Bose-Einstein Condensates
- Approximations and Bounds for Eigenvalues of Elliptic Operators
- A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates