Posts
“The Shapes of Things: A Practical Guide to Differential Geometry and the Shape Derivative” provides clear geometric formulas that can be used to understand mathematical models that contain geometric differential equations, or PDEs.
Walker researches PDEs for fluids and free or moving boundaries as they pertain to geometric evolution problems as well as numerical analysis and finite element methods, mesh generation and optimal PDE control of shape.
“The Shapes of Things” is a reference book that may be helpful for students and scientists using surface geometry and shape optimization in their work.
The book was derived from Walker’s lecture notes, which he created and refined while teaching a special topics course at LSU in 2011.
“Eventually, after sharing the notes I realized their potential value to others and sought to create this book to make shape derivatives accessible to a broader audience,” wrote Walker in the book’s preface.
The book was published by SIAM, the Society for Industrial and Applied Mathematics.
About the Author
Shawn W. Walker is an assistant professor of mathematics at Louisiana State University (LSU), with a joint appointment in the Center for Computation and Technology (CCT). He held a postdoctoral position at the Courant Institute (New York University) and joined the LSU faculty in 2010 in the computational mathematics group. He is a member of SIAM, AMS, MRS, and APS. His research interests include PDEs for fluids and moving/free boundaries, geometric evolution problems, numerical analysis and finite element methods, mesh generation, and optimal PDE control of shape.
Additional Link:
“The Shapes of Things: A Practical Guide to Differential Geometry and the Shape Derivative” http://bookstore.siam.org/dc28/
Source: Louisiana State University
