Nagoya University: A Rich Society Opened Up by Computer Simulation

A Rich Society Opened Up by Computer Simulations

As part of my research on the boundary element method, I conducted studies on: 1) solving sequential shape optimization problems using the boundary element method, 2) optimal design of coil spring cross-sectional shapes using the boundary element method, and 3) research on adaptive mesh methods in the boundary element method. Additionally, I authored a text for engineering beginners on the boundary element method and finite element method titled "Numerical Methods for Partial Differential Equations," as well as a related text on linear algebra titled "Linear Algebra for Computation." The Trefftz method is a boundary-type analysis method, but it differs in that it uses integral equations without singularities. Therefore, I advanced research on the engineering applications of the Trefftz method, including: 1) proposing a sensitivity analysis method using the Trefftz method, 2) proposing a higher-order design sensitivity analysis method using the Trefftz method, 3) proposing an adaptive mesh method for the Trefftz method, 4) simulating the sloshing phenomenon of water surface waves using the Trefftz method, and 5) conducting thermal conduction analysis of functionally graded materials using the Trefftz method. I served as a guest editor for a special issue commemorating the 70th anniversary of the Trefftz method in an international journal. I also authored "Introduction to the Trefftz Method."

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