We discuss the automatic creation and adaptive refinement of an unstructured mesh within a complex geometry such as the space surrounding an airplane. This may be formulated as two distinct parts; a non-parallel part requiring global knowledge which automatically creates a coarse compatible mesh, and a parallel local refinement algorithm, which refines the mesh until simulation can begin, then ...

One aspect of adaptive mesh refinement in the finite element method for solving partial differential equations is the method by which elements are refined. In the early 1980’s the dominant method for refining triangles was the red-green algorithm of Bank and Sherman. The red refinements are the desired refinements, but will result in an incompatible mesh when used alone. The green refinements a...

In this work, simulations with scalene triangle meshes represented by a recently proposed graphbased adaptive mesh refinement technique are described. Previously, simulations exclusively with isosceles right triangles were presented with this graph-based scheme. This data structure represents triangular meshes in finite-volume discretizations in order to solve second-order partial differential ...

This paper describes an adaptive mesh refinement algorithm for improving the accuracy in the solution of electromagnetic problems in transmission lines. A residual error indicator is used for detecting the refinement zones, and two h-refinement techniques for triangular meshes (the longest edge bisection and the regular split) are applied for increasing the degrees of freedom in the mesh. This ...

In this paper, we discuss some of the issues in obtaining high performance for block-structured adaptive mesh refinement software for partial differential equations. We show examples in which AMR scales to thousands of processors. We also discuss a number of metrics for performance and scalability that can provide a basis for understanding the advantages and disadvantages of this approach.

The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference discretizations of wave-like equations using characteristic coordinates. We demonstrate the algorithm by constructing a code implementing the Einstein-Klein-Gordon sy...

An analysis of the electromagnetic field based on adaptive finite element is presented in this paper. The performance of the adaptive algorithms, based on an element-element h-refinement technique, is assessed. The features of the refinement indictors, adaptation criteria and error estimation parameters are discussed. The strategy of the adaptive mesh refinement method applied to the eigenvalue...