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Conference Proceeding

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A new method called Augmented Matched Interface and Boundary (AMIB) has been developed to solve partial differential equation models, such as the heat equation, over irregular two-dimensional domains. The original AMIB method features unique numerical treatments to solve problems with various boundary conditions and shapes, resulting in highly accurate and efficient numerical solutions. However, recent numerical experiments have revealed that the original AMIB method can fail when dealing with sharply curved boundaries. To address this issue, new numerical techniques have been introduced in our latest work to enhance the robustness of the AMIB method. These techniques have been numerically verified to improve the accuracy and efficiency of the AMIB method when solving various problems with sharply curved boundaries. Due to its success, we plan to use this method to simulate Magnetic Fluid Hyperthermia (MFH) cancer treatment by solving the Pennes Bioheat Equation on a domain that consists of a tumor and the surrounding healthy tissue.