Binarized-octree generation for Cartesian adaptive mesh refinement around immersed geometries

We revisit the generation of balanced octrees for adaptive mesh refinement (AMR) of Cartesian domains with immersed complex geometries. In a recent short note (Hasbestan and Senocak, 2017) [42], we showed that the data locality of the Z-order curve in a hashed linear-octree generation method may not be perfect because of potential collisions in the hash table. Building on that observation, we propose a binarized-octree generation method that complies with the Z-order curve exactly. Similar to a hashed linear-octree generation method, we use Morton encoding to index the nodes of an octree, but use a red-black tree in place of the hash table. Red-black tree is a special kind of a binary tree, which we use for insertion and deletion of elements during mesh adaptation. By strictly working with the bitwise representation of an octree, we remove computer hardware limitations on the depth of adaptation on a single processor. Additionally, we introduce a geometry encoding technique for rapidly tagging a solid geometry for mesh refinement. Our results for several geometries with different levels of adaptations show that the binarized-octree generation method outperforms the linear-octree generation method in terms of runtime performance at the expense of only a slight increase in memory usage. The current AMR capability, rebl-AMR, is available as open-source software

Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability

An open and parallel multiresolution framework using block-based adaptive grids

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source

A parallel solution-adaptive scheme for ideal magnetohydrodynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77232/1/AIAA-1999-3273-200.pd