Adaptive grid generation is an active research topic for numerical solution of differential equations. In this paper, we propose a variational method which generates transformations with prescribed Jacobian determinant and curl. Then we use this transformation to achieve adaptive grid generation task.
Averaging diffeomorphisms is a challenging problem, and it has great applications in areas like medical image atlases. The simple Euclidean average can neither guarantee the averaged transformation is a diffeomor-phism, nor get reasonable result when there is a local rotation. The goal of this paper is to propose a new approach to averaging diffeomorphisms… (More)
Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace research community is working on next generation of CFD capacity that is accurate, automatic, and fast. A key component of the next generation of CFD is a greatly enhanced capacity for mesh generation and adaptivity of the mesh… (More)
Several new techniques based on the deformation method are reported. These include techniques for domains with moving boundaries , boundary fitted triangulation with prescribed boundary nodes, adaptation of multi-block meshes and curvilinear triangular meshes. c 2015 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing… (More)
In the first part of this paper, various versions of the deformation method for grid adaptation and their applications are described. The main result of the paper is contained the second part. In particular, based on the deformation method, we propose a method of reconstructing any differentiable, invertible transformation on a square or a cube. 2 1.… (More)