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Full-Text Articles in Physical Sciences and Mathematics
A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, Kumudu Gamage, Yan Peng
A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, Kumudu Gamage, Yan Peng
College of Sciences Posters
Parabolic interface problems have many applications in physics and biology, such as hyperthermia treatment of cancer, underground water flow, and food engineering. Here we present an algorithm for solving two-dimensional parabolic interface problems where the coefficient and the forcing term have a discontinuity across the interface. The Crank-Nicolson scheme is used for time discretization, and the direct immersed interface method is used for spatial discretization. The proposed method is second order in both space and time for both solution and gradients in maximum norm.
A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng
A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng
College of Sciences Posters
Interface problems have many applications in fluid dynamics, molecular biology, electromagnetism, material science, heat distribution in engines, and hyperthermia treatment of cancer. Mathematically, interface problems commonly lead to partial differential equations (PDE) whose in- put data are discontinuous or singular across the interfaces in the solution domain. Many standard numerical methods designed for smooth solutions poorly work for interface problems as solutions of the interface problems are mostly non-smoothness or discontinuous. Moving interface problems depends on the accuracy of the gradient of the solution at the interface. Therefore, it became essential to derive a method for interface problems that gives …