Stochastic domain decomposition for time dependent adaptive mesh generation

@article{Bihlo2015StochasticDD,
  title={Stochastic domain decomposition for time dependent adaptive mesh generation},
  author={Alexander Bihlo and Ronald Dale Haynes and E. J. Walsh},
  journal={arXiv: Numerical Analysis},
  year={2015}
}
The efficient generation of meshes is an important component in the numerical solution of problems in physics and engineering. Of interest are situations where global mesh quality and a tight coupling to the solution of the physical partial differential equation (PDE) is important. We consider parabolic PDE mesh generation and present a method for the construction of adaptive meshes in two spatial dimensions using stochastic domain decomposition that is suitable for an implementation in a multi… Expand

Figures and Tables from this paper

Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems
TLDR
This work presents an efficient moving mesh method for the simulation of fourth order nonlinear partial differential equations (PDEs) in two dimensions using the Parabolic Monge–Ampere (PMA) equation and establishes several new results and conjectures on the nature of self-similar singularity formation in higher order PDEs. Expand
Hybrid PDE solver for data-driven problems and modern branching†
TLDR
The purpose of this paper is to spread awareness of the Probabilistic Domain Decomposition (PDD) method, a fresh approach to the parallelization of PDEs with excellent scalability properties that exploits the stochastic representation of the PDE and its approximation via Monte Carlo in combination with deterministic high-performance PDE solvers. Expand
On the Stochastic / Deterministic Numerical Solution of Composite Deterministic Elliptic PDE Problems *
We consider stochastic numerical solvers for deterministic elliptic Partial Differential Equation (PDE) problems. We concentrate on those that are characterized by their multidomain or/andExpand
Probabilistic domain decomposition for the solution of the two-dimensional magnetotelluric problem
Probabilistic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell’s equations as used in the magnetotelluric method. The domain is split into non-overlappingExpand
Stochastic domain decomposition for the solution of the two-dimensional magnetotelluric problem
Stochastic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The stochastic form of the exact solution ofExpand
Massively parallel stochastic solution of the geophysical gravity problem
In this paper, we report the advantages of using a stochastic algorithm in the context of mineral exploration based on gravity measurements. This approach has the advantage over deterministic methodsExpand
DeepLM: Large-scale Nonlinear Least Squares on Deep Learning Frameworks using Stochastic Domain Decomposition
  • Jingwei Huang, Shan Huang, Mingwei Sun
  • 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
  • 2021
We propose a novel approach for large-scale nonlinear least squares problems based on deep learning frameworks. Nonlinear least squares are commonly solved with the Levenberg-Marquardt (LM) algorithmExpand

References

SHOWING 1-10 OF 36 REFERENCES
Parallel stochastic methods for PDE based grid generation
TLDR
This work considers elliptic PDE based mesh generation and presents a method for the construction of adaptive meshes in two spatial dimensions using domain decomposition that is suitable for an implementation on parallel computing architectures. Expand
A Stochastic Domain Decomposition Method for Time Dependent Mesh Generation
TLDR
A stochastic domain decomposition (SDD) method to find adaptive meshes for steady state problems by solving a linear elliptic mesh generator by reducing the number of Monte-Carlo simulations required. Expand
Domain Decomposition Approaches for Mesh Generation via the Equidistribution Principle
TLDR
This paper proposes several Schwarz domain decomposition algorithms for the generation of time dependent (moving) equidistributing grids, and studies in detail the convergence properties of these algorithms applied to the nonlinear mesh PDE in one spatial dimension. Expand
Anr-Adaptive Finite Element Method Based upon Moving Mesh PDEs
TLDR
A fully developedr-adaptive finite element method can be expected to be ideally suited to complement the currently popularh-pfinite element methods and to provide increased reliability and efficiency for mesh adaptation. Expand
A Moving-Mesh Finite Element Method and its Application to the Numerical Solution of Phase-Change Problems
A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to de- termine nodal meshExpand
A moving mesh finite element method for the two-dimensional Stefan problems
An r -adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two-dimensional heat conduction problems with a phase change. The grid is obtained from aExpand
Domain Decomposition Solution of Elliptic Boundary-Value Problems via Monte Carlo and Quasi-Monte Carlo Methods
Domain decomposition of two-dimensional domains on which boundary-value elliptic problems are formulated is accomplished by probabilistic (Monte Carlo) as well as by quasi-Monte Carlo methods,Expand
A two-dimensional moving finite element method with local refinement based on a posteriori error estimates
In this paper, we consider the numerical solution of time-dependent PDEs using a finite element method based upon rh-adaptivity. An adaptive horizontal method of lines strategy equipped with aExpand
An adaptive mesh redistribution algorithm for convection-dominated problems
Convection-dominated problems are of practical applications and in general may require extremely fine meshes over a small portion of the physical domain. In this work an efficient adaptive meshExpand
Numerical Solution of the Quasilinear Poisson Equation in a Nonuniform Triangle Mesh
A finite-difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two-dimensional Poisson equation�·(���) +S= 0, where � is a function of �Expand
...
1
2
3
4
...