Oscillatory behaviour of the RBF-FD approximation accuracy under increasing stencil size
Jožef Stefan Institute（约瑟夫·斯蒂芬研究所）；Parallel and Distributed Systems Laboratory（并行与分布式系统实验室）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；Jožef Stefan International Postgraduate School（约瑟夫·斯蒂芬国际研究生院）
Andrej Kolar-Požun, Mitja Jančič, Miha Rot, Gregor Kosec
When solving partial differential equations on scattered nodes using the Radial Basis Function generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs with monomial augmentation, we observe that it affects the approximation accuracy in a particularly interesting way - the solution error oscillates under increasing stencil size. We find that we can connect this behaviour with the spatial dependence of the signed approximation error. Based on this observation we are then able to introduce a numerical quantity that indicates whether a given stencil size is locally optimal.
Some observations regarding the RBF-FD approximation accuracy dependence on stencil size
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；University of Ljubljana, Faculty of Mathematics and Physics（卢布尔雅那大学数学与物理学院）；International Postgraduate School Jožef Stefan（约瑟夫·斯特凡国际研究生院）
Numerical Stability on Local Integral Methods using RBF-QR
Faculty of Exact Sciences, Engineering and Surveying,National University of Rosario（罗萨里奥国立大学精确科学、工程与测量学院）；French Argentine International Centerfor Information and Systems Sciences,UAM (France)/UNR-CONICET（法阿国际信息与系统科学中心，法国UAM/罗萨里奥国立大学-阿根廷国家科学研究委员会）
RBF-Generated Finite Difference Method Coupled with Quadratic Programming for Solving PDEs on Surfaces with Derivative Boundary Conditions
School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）；Institute of Mathematical Sciences, ShanghaiTech University（上海科技大学数学科学学院）；School of Mathematics, University of Minnesota（明尼苏达大学数学学院）
Adaptive hyperviscosity stabilisation for the RBF-FD method in solving advection-dominated transport equations
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Jozef Stefan International Postgraduate School（约瑟夫·斯特凡国际研究生院）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）
High order multiscale methods for advection-diffusion equation in highly oscillatory regimes: application to surfactant diffusion and generalization to arbitrary domains
A High-Order Compact Finite Volume Method for Unstructured Grids: Scheme Space Formulation and One-Dimensional Implementations
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics, School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学系、力学与工程科学学院湍流与复杂系统国家重点实验室）
