Mathematical Modeling and Simulation
暫譯: 數學建模與模擬

這本教科書適合對數學建模和模擬感興趣的學士/碩士學生。它將分析、微積分和數值方法整合在一個連貫的卷冊中。

特別關注工程數學，涵蓋建模、分析、方法開發、算法的實現與測試，以及應用於實際問題和對結果的批判性解釋。這本書可以在學士課程和部分碩士課程中使用，提供一套全面的課程，將形式抽象思維與直觀的模型形成、關鍵算法開發和結果解釋相連結。書中包含來自物理、技術、生物和化學的眾多實際應用範例。它還介紹了用於算法開發和計算分析的 Matlab 和 C 語言。書中包含了軟體和選定問題的解決方案。

Bernard Geurts is the Chair of the Multiscale Modeling and Simulation (MMS) group at the University of Twente, The Netherlands. The big dream behind their work is to help open entirely new worlds of understanding and application in science and technology, by creating advanced computational methods. The impact of their work is increased by close collaboration with other disciplines.The main research focus is on the mathematical development of computational methods forsystems of nonlinear differential equations. The models studied at MMS represent complexphysical mechanisms acting simultaneously at micro- and macro scales. Much of the workis motivated by fluid-mechanical problems, from nano- and micro fluidics to macroscopicturbulence.The three directions of MMS expertise, i.e., (i) mathematical models, (ii) numerical methods and (iii) advanced reduction and regularisation techniques, are exploited in multi-disciplinary research. The work is characterised by balancing fundamental orientation and application perspective. Specific targets are derived from unresolved issues in science and technology.Main application areas are in fluid technology, health and energy such as: - multi-phase turbulence and heat transfer, - aerosol formation and phase transitions, - biomedical flows in complex domains, - nano-engineered materials for energy systemsSpecific challenges range from understanding the physics of boiling and turbulence modulation, to novel methods of controlled respiratory drug delivery. Moreover, new methods are forgedfor the prediction and mitigation of cerebral haemorrhages and the optimisation of nanostructured inclusions for new materials in energy harvesting.While these applications and research fields appear diverse, the binding element is his interest in mathematical elegance and abstraction to discover and exploit the simplicity behind apparent complexity in physical systems.
Ruud van Damme is associate professor in numerical analysis in the Multiscale Modeling and Simulation. This group is part of the Department of Applied Mathematics at the University of Twente.

His research interests are in mathematics, physics and numerics. The main topics lie in fields such as fluid mechanics, quantum mechanics, graph theory and stochastic processes. His recent research concentrates on advanced numerical techniques and their application, such as splines and wavelets, adaptive grid methods and high dimensional integration.

伯納德·格爾茨是荷蘭特溫特大學多尺度建模與模擬（MMS）小組的主席。他們工作的宏大夢想是通過創造先進的計算方法，幫助開啟科學和技術中全新的理解與應用世界。他們工作的影響力因與其他學科的緊密合作而增強。主要的研究重點是針對非線性微分方程系統的計算方法進行數學發展。MMS研究的模型代表了在微觀和宏觀尺度上同時作用的複雜物理機制。許多工作受到流體力學問題的驅動，從納米和微米流體學到宏觀湍流。MMS的三個專業方向，即（i）數學模型，（ii）數值方法和（iii）先進的降維和正則化技術，均在多學科研究中得到應用。這項工作以平衡基礎導向和應用視角為特徵。具體目標源自科學和技術中未解決的問題。主要應用領域包括流體技術、健康和能源，例如：- 多相湍流和熱傳遞，- 氣溶膠形成和相變，- 複雜領域中的生物醫學流動，- 用於能源系統的納米工程材料。具體挑戰範圍從理解沸騰和湍流調制的物理學，到新型的控制呼吸藥物釋放方法。此外，還開發了預測和減輕腦出血的新的方法，以及優化納米結構夾雜物以用於新材料的能量收集。雖然這些應用和研究領域看似多樣，但其共同的元素是他對數學優雅和抽象的興趣，以發現和利用物理系統中表面複雜性背後的簡單性。

魯德·范達梅是多尺度建模與模擬中的數值分析副教授。該小組隸屬於特溫特大學應用數學系。

他的研究興趣涵蓋數學、物理和數值分析。主要主題涉及流體力學、量子力學、圖論和隨機過程等領域。他最近的研究集中在先進的數值技術及其應用上，例如樣條和小波、自適應網格方法和高維積分。