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This article presents a modified butterfly subdivision scheme with improved smoothness over regular triangular meshes. The proposed technique is an approximating scheme with a tension parameter. It achieves fourth-order accuracy and generates C 2 limit surfaces for a suitable range of the parameter while maintaining the same support of the original butterfly scheme. To validate the theoretical results, some numerical examples are provided. [ABSTRACT FROM AUTHOR]

Abstract: A butterfly‐based hierarchical LU factorization scheme for solving the PMCHWT equations for analyzing scattering from homogenous dielectric objects is presented. The proposed solver judiciously re‐orders the discretized integral operator and butterfly‐compresses blocks in the operator and its LU factors. The observed memory and CPU complexities scale as O(N log2N) and O(N1.5 log N), respectively. The proposed solver is applied to the analyses of scattering several large‐scale dielectric objects. [ABSTRACT FROM AUTHOR]

A butterfly-based direct combined-field integral-equation (CFIE) solver for analyzing scattering from electrically large, perfect electrically conducting objects is presented. The proposed solver leverages the butterfly scheme to compress blocks of the hierarchical LU-factorized discretized CFIE operator and uses randomized butterfly reconstruction schemes to expedite the factorization. The memory requirement and computational cost of the direct butterfly-CFIE solver scale as O(N\log ^2N) and O(N^1.5\log N) , respectively. These scaling estimates permit significant memory and CPU savings when compared to those realized by low-rank decomposition-based solvers. The efficacy and accuracy of the proposed solver are demonstrated through its application to the analysis of scattering from canonical and realistic objects involving up to 14 million unknowns. [ABSTRACT FROM AUTHOR]

We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many spectrum maximizing products. A criterion of convergence of the algorithm is proved. As an application we solve two challenging computational open problems. First we find the regularity of the Butterfly subdivision scheme for various parameters ω. In the "most regular" case ω = 1/16 , we prove that the limit function has Hölder exponent 2 and its derivative is "almost Lipschitz" with logarithmic factor 2. Second we compute the Hölder exponent of Daubechies wavelets of high order. [ABSTRACT FROM AUTHOR]

The objective of this paper is to propose an efficient model-based bit allocation process optimizing the performances of a wavelet coder for semiregular meshes. More precisely, this process should compute the best quantizers for the wavelet coefficient subbands that minimize the reconstructed mean square error for one specific target bitrate. In order to design a fast and low complex allocation process, we propose an approximation of the reconstructed mean square error relative to the coding of semiregular mesh geometry. This error is expressed directly from the quantization errors of each coefficient subband. For that purpose, we have to take into account the influence of the wavelet filters on the quantized coefficients. Furthermore, we propose a specific approximation for wavelet transforms based on lifting schemes. Experimentally, we show that, in comparison with a "naïve" approximation (depending on the subband levels), using the proposed approximation as distortion criterion during the model-based allocation process improves the performances of a wavelet-based coder for any model, any bitrate, and any lifting scheme. [ABSTRACT FROM AUTHOR]