Fast operator splitting methods for obstacle problems
Journal of Computational Physics, ISSN: 0021-9991, Vol: 477, Page: 111941
2023
- 2Citations
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Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
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Metrics Details
- Citations2
- Citation Indexes2
Article Description
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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0021999123000360; http://dx.doi.org/10.1016/j.jcp.2023.111941; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85146865388&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0021999123000360; https://dx.doi.org/10.1016/j.jcp.2023.111941
Elsevier BV
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