Efficient numerical solution of the inverse Stefan problems using the method of fundamental solutions

• Grant number: 16/19648-9
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): December 01, 2016
• Effective date (End): February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: José Alberto Cuminato
• Grantee: Gujji Murali Mohan Reddy
• Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

The method of fundamental solutions is a relatively new method for the numerical solution of certain partial differential equations in which a fundamental solution of the operator in the governing equation is known explicitly. The ease with which it can be implemented and its effectiveness have made it a very popular tool for the solution of a largevariety of problems arising in Science and Engineering. In recent years, it has been used extensively for an important class of problems, namely inverse problems. As the accuracy of the approximation obtained by using the method of fundamental solutions depends on the location of the sources, in order to obtain a satisfactorily accurate approximation, one needs to place the sources in an appropriate way. A practical way of achieving this with minimal computational cost is yet to be found for inverse Stefan problems. This proposal seeks funding for a postdoctoral project in view of the growing interest in this area. The project will develop Mathematical analysis and numerical methods to gain understanding of this approach and will focus in particular on the one and multi phase inverse Stefan problems. A part of this work will be in collaboration with Dr. Michael Vynnycky from the Royal Institute of Technologyin Stockholm, Sweden, and will complement, and interact with other modelling projects those are being carried out there. (AU)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

REDDY, G. MURALI MOHAN; SINHA, RAJEN KUMAR; CUMINATO, JOSE ALBERTO. A Posteriori Error Analysis of the Crank-Nicolson Finite Element Method for Parabolic Integro-Differential Equations. JOURNAL OF SCIENTIFIC COMPUTING, v. 79, n. 1, p. 414-441, APR 2019. Web of Science Citations: 0.

REDDY, G. M. M.; VYNNYCKY, M.; CUMINATO, J. A. An efficient adaptive boundary algorithm to reconstruct Neumann boundary data in the MFS for the inverse Stefan problem. Journal of Computational and Applied Mathematics, v. 349, p. 21-40, MAR 15 2019. Web of Science Citations: 0.

REDDY, G. M. M.; VYNNYCKY, M.; CUMINATO, J. A. On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems. Inverse Problems in Science and Engineering, v. 26, n. 9, p. 1249-1279, 2018. Web of Science Citations: 1.

VYNNYCKY, M.; REDDY, G. M. M. On the Effect of Control-Point Spacing on the Multisolution Phenomenon in the P3P Problem. MATHEMATICAL PROBLEMS IN ENGINEERING, 2018. Web of Science Citations: 0.