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There are numerous applications for which the geometric domain moves as a function of time, e.g., flapping airplane wings, a beating heart, and clothing moving in the wind. A dynamic sequence of meshes is required in order to capture the changing geometry.

In the first part of the talk, I will present parallel LBWARP, a parallel log barrier-based tetrahedral mesh warping algorithm for distributed memory machines. The algorithm is a general-purpose, geometric dynamic meshing algorithm that parallelizes the sequential LBWARP algorithm by Shontz and Vavasis. The algorithm solves a large global system of linear equations in parallel to determine where to move the interior nodes of the mesh. This computation is based on the representation of the initial mesh and the deformation provided by the user. A log-barrier interior point method is used to solve several convex optimization problems to determine the representation of the initial mesh. Sparse linear solvers for problems with multiple right-hand sides are used to solve the global systems of linear equations corresponding to multiple warping steps. I will present several numerical examples which demonstrate the excellent scalability properties of the method.

In the second part of the talk, I will present LBWARP2Gen, a high-order curvilinear tetrahedral mesh generation algorithm. The algorithm generates a second-order mesh by deforming a linear tetrahedral mesh into a high-order mesh based on the LBWARP method. The solution methodology includes the use of a sequential quadratic programming method (to determine the representation of the initial mesh) and a log-barrier interior point method (to determine the projection of the midpoints onto the boundary of the geometry). I will present numerical examples demonstrating the success of the method in generating high-quality meshes and will show how the method can be used to generate dynamic meshes, as well.

Parts of this talk represent joint work by Thap Panitanarak, The Pennsylvania State University, and Michael Stees, University of Kansas.