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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i4.40
pages 397-409

Adaptive Multiwavelet-Hierarchical Method for Multiscale Computation

Youming Wang
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, People’s Republic of China, 710049
Xuefeng Chen
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, People’s Republic of China, 710049
Zhengjia He
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, People’s Republic of China, 710049

ABSTRACT

An adaptive multiwavelet-hierarchical method characterized by high convergent rate and flexible adaptive strategy is proposed for multiscale computation of field problems. According to the Strang--Fix condition, the convergence rate of the finite element multiwavelet method is determined by the approximation order of scaling functions in the same level of multiwavelet refinement. To raise the approximation order of scaling functions, finite element multiwavelets are combined with hierarchical bases to construct a new multilevel multiwavelet-hierarchical space. An adaptive strategy for multiwavelet-hierarchical refinement is presented based on new error estimation in the form of multiwavelets and hierarchical bases, which leaves much freedom for the problem-oriented selection of multiwavelets or hierarchical functions. Numerical examples demonstrate that the proposed method is an accurate and efficient tool in solving the field problems with singularities or changes in high gradients.

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