.png){kind=icon}
Return
Fast operator splitting methods for obstacle problems
.png){kind=icon}
OA
AI
DOI：10.1016/j.jcp.2023.111941.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the linear and nonlinear obstacle problems. The proposed methods have three ingredients: (i) Utilize an indicator function to formularize the constrained problem as an unconstrained problem, and associate it to an initial value problem. The obstacle problem is then converted to solving for the steady state solution of an initial value problem. (ii) An operator-splitting strategy to time discretize the initial value problem. After splitting, a heat equation with obstacles is solved and other subproblems either have explicit solutions or can be solved efficiently. (iii) A new constrained alternating direction explicit method, a fully explicit method, to solve heat equations with obstacles. The proposed methods are easy to implement, do not require to solve any linear systems and are more efficient than existing numerical methods while keeping similar accuracy. Extensions of the proposed methods to related free boundary problems are also discussed.(c) 2023 Elsevier Inc. All rights reserved.
Keywords:
Obstacle problem
Operator splitting methods
Alternating direction explicit method
Nonlinear elliptic equations
Free boundary
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
3.8
Papers:
1.6W
Citations:
7.4W
Organization
Cited Papers
ShareSaveAn Implementation Scheme of Range and Angular Measurements for FMCW MIMO Radar via Sparse Spectrum Fitting.png)
ElectronicsOAAI
ElectronicsIF0
OAAIShareSaveShareSaveMolecular phylogeny of mangroves II. Intra -and inter-specific variation in Avicennia revealed by RAPD and RFLP markersGenome
GenomeIF0
PREAI
ShareSaveShareSave
View more