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Kumudu Gamage, visiting assistant professor of mathematics at Washington and Lee University, recently coauthored an article titled “A Direct Method for Solving Three-Dimensional Elliptic Interface Problems” which appeared in the peer-reviewed International Journal of Numerical Analysis and Modeling.
Gamage collaborated on the article with professor Zhilin Li from North Carolina State University and professor Yan Peng, her doctoral adviser from Old Dominion University. Together, the authors present a direct method for efficiently solving three-dimensional elliptic interface problems featuring piecewise constant coefficients with a finite jump across the interface.
“Interface problems are significant because they exist at the boundary between two different materials or varying states of the same material,” said Gamage. “These problems have numerous practical applications, including fluid dynamics, electromigration of voids, glacier prediction, growth of internal blood clots and thermodynamics. This paper presents a novel computational approach that enhances the accuracy and efficiency of solving elliptic interface problems in three dimensions. The method’s simplicity and effectiveness make it accessible to a broad range of researchers.”
The authors present an approach that avoids augmented variables, distinguishing it from traditional methods. The computational framework relies on a finite difference scheme implemented on a uniform Cartesian grid system. By utilizing a seven-point Laplacian for grid points away from the interface, their method only requires coefficient modifications for grid points located near or on the interface. Numerical experiments serve to validate their method’s effectiveness. Generally, it achieves second-order accuracy for both the solution and its gradient, measured in the maximum norm, and is particularly effective in scenarios with moderate coefficient jumps. Extending and building upon the recent work of elliptic interfaces, their approach successfully introduces a simpler method for extension into three dimensions.
Gamage joined the faculty as a visiting assistant professor at the start of the 2022-23 academic year. She holds a Bachelor of Science in mathematics (honors) from the University of Kelaniya (Sri Lanka) and a pair of Master of Science degrees, one in sustainable environment and energy systems from Middle East Technical University (Turkey) and another in mathematics from Old Dominion. She also earned a doctorate in computational applied mathematics from ODU.
