The Dual Mesh Control Domain Method: A Marriage of the Finite Element and Finite Volume Methods

The finite element method (FEM) and finite volume method (FVM) are widely used numerical techniques for solving differential equations, with FEM mainly applied in solid mechanics and FVM in heat transfer and fluid dynamics. Both methods have drawbacks: FEM can lead to discontinuities at element interfaces unless C1-continuous approximations are used, while FVM relies on ad-hoc techniques from finite difference methods, lacking explicit approximations and concepts of duality. In 2019, Reddy introduced the dual mesh control domain method (DMCDM), combining features of both FEM and FVM. DMCDM uses a primal mesh for dependent variable interpolation and a dual mesh for integral satisfaction of governing equations, enhancing the methods’ effectiveness. This lecture discusses DMCDM’s key features and demonstrates its applications in various linear and nonlinear problems.

Speaker: Prof J N Reddy

Biography: 

Dr. Reddy is a Distinguished Professor and Regents’ Professor at Texas A&M University, holding the O’Donnell Foundation Chair IV in Mechanical Engineering. An ISI highly cited researcher, he has authored 25 textbooks and over 800 journal papers, making significant contributions to applied mechanics, particularly through his shear deformation theories, including the Reddy third-order plate theory and Reddy layerwise theory. These theories have influenced commercial finite element software like ABAQUS and NISA. Recently, his research has focused on locking-free shell finite elements and nonlocal continuum mechanics related to architected materials and structural failures. Dr. Reddy has received numerous prestigious awards, including the 2023 Leonardo da Vinci Award, the 2023 Michael Païdoussis Medal, and the 2019 SP Timoshenko Medal, among others. He is a member of eight national academies, including the U.S. National
Academy of Engineering, and a foreign fellow of several international engineering academies.