Solving higher order PDEs with isogeometric analysis on implicit domains using weighted extended THB-splines
| Autor: | Jiansong Deng, Tianhui Yang, Ammar Qarariyah |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Partial differential equation
Adaptive refinement Aerospace Engineering 020207 software engineering Basis function 02 engineering and technology Isogeometric analysis 01 natural sciences Computer Graphics and Computer-Aided Design 0104 chemical sciences 010404 medicinal & biomolecular chemistry Spline (mathematics) Reentrancy Modeling and Simulation Automotive Engineering 0202 electrical engineering electronic engineering information engineering Biharmonic equation Applied mathematics Mathematics |
| Zdroj: | Computer Aided Geometric Design. 71:202-219 |
| ISSN: | 0167-8396 |
| Popis: | We study the numerical solution for higher order partial differential equations defined on implicit domains. We represent isogeometric analysis on implicit domains and construct weighted extended truncated hierarchical B-splines. Specifically, the spline basis functions are classified, according to the cells occupied by their support inside the domain, using a level by level classification mechanism. A hierarchical extension is then proposed to connect basis functions with small support in the computational domain to more stable basis inside the domain. The basis functions are formulated to acquire local adaptive refinement and preserve stability to release the full approximation power. A numerical illustration is performed to solve the Biharmonic equation on a number of implicit domains with holes and reentrant corners. The error results and condition numbers of the numerical examples reflect the potential of the approach. |
| Databáze: | OpenAIRE |
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