We present an approach to solving hyperbolic conservation laws by finitevolume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a bloc...

A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space combined with detailed mechanisms for accommodating the adapting grids ensure that conservation is maintained a...

Neurofuzzy systems—the combination of artificial neural networks with fuzzy logic—have become useful in many application domains. However, conventional neurofuzzy models usually need enhanced representational power for applications that require context and state (e.g., speech, time series prediction, control). Some of these applications can be readily modeled as finite state automata. Previousl...

In this note, we discuss how to efficiently evaluate and assemble general finite element variational forms on H(div) and H(curl). The proposed strategy relies on a decomposition of the element tensor into a precomputable reference tensor and a mesh-dependent geometry tensor. Two key points must then be considered: the appropriate mapping of basis functions from a reference element, and the orie...

A regular paving is a finite succession of bisections that partition a root box x in R into sub-boxes using a binary tree-based data structure. We extend regular pavings to mapped regular pavings which map sub-boxes in a regular paving of x to elements in some set Y. Arithmetic operations defined on Y can be extended point-wise over x and carried out in a computationally efficient manner using ...

Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The best-known example of this type is the Hermite functions, i.e., the Hermite polynomials multiplied by exp(−x2/2), which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a com...