Interviews with Faculty Researchers

– Interview with Prof. Li Buyang
Professor, Department of Applied Mathematics
Awardee of the Faculty Award for Outstanding Achievement 2023 - Research and Scholarly Activities: Outstanding Young Researcher

Computational mathematics is a multifaceted field that involves developing algorithms to enhance the accuracy and quality of computations. It encompasses complex tasks such as discretizing two- and three-dimensional objects, solving large-scale linear or nonlinear systems, and addressing challenges related to solving partial differential equations. Prof. Li Buyang's research project on curvature-driven surface evolution aims to develop new mathematical analyses and novel algorithms for computing surface evolution processes that seamlessly integrate geometrical and physical aspects in various contexts.

Surface evolution encompasses a diverse range of phenomena, from gas bubble motion in liquids to deformations in materials used in electronic devices. The potential applications are extensive and impactful, particularly in the development of new materials capable of withstanding adverse conditions in electronic devices. Numerical simulations play a vital role in understanding how these surfaces change under different conditions. Many pre-existing methods of computing surface evolution rely on intuitions and heuristic arguments, often lacking the mathematical rigor for accurate computations.

Prof. Li’s research delves deeply into the mathematics of computation, concentrating on the development of novel mathematical analysis for a class of algorithms that share some common features underlying surface evolution, disclosing previously unknown structures of the underlying geometric partial differential equations, and providing valuable insights for understanding and improving the stability and accuracy of these algorithms. The newfound understanding contributes to developing novel algorithms that could improve the accuracy and stability of computational methods, ultimately enhancing the reliability and quality of numerical simulations.

由曲率驅動的表面演化之嶄新運算方法及其應用

– 李步揚教授專訪
應用數學系教授
2023年學院特設傑出成就獎 –研究及學術活動 (傑出青年研究員)得獎者

計算數學是一門橫跨多個領域的研究方向，旨在發展一系列數值計算方法來提高人們對各類科學和工程問題進行數值計算仿真的精確性和效率，其中包括二維空間和三維空間的離散、求解大規模線性或非線性的方程組，以及求解偏微分方程組等充滿挑戰的複雜問題。由 李步揚教授主導的曲率驅動的曲面演化研究項目，旨在發展新的數值分析理論和計算方法來求解和模擬各種幾何及物理情境中的曲面演化過程。

曲面演變包括從液體中的氣泡運動到電子設備中使用的材料的變形等各種各樣的現象，具有廣泛的潛在應用。數值模擬在理解曲面在不同條件下的變化方面發揮著至關重要的作用。目前，不少相關的計算方法和數值格式仍依賴於直覺來設計，相關計算方法的準確性和誤差估計等研究仍處於探索階段，缺少數學上的嚴格論證。

李教授對計算數學和計算曲率流的深入研究，旨在為幾類具有共同特徵的曲面演化過程，透過數學分析找出描述曲面演化的幾何偏微分方程中的一些未知結構。這些嶄新的理解開發出可提高準確性和穩定性的計算方法，從而增強數值模擬的可靠性和質量。