2024/03/11 by Jielin Yang, Suchuan Dong, Yang, Jielin +1
Computer Science · Engineering · #Composite Structure Analysis and Optimization #Contact Mechanics and Variational Inequalities #Dynamics and Control of Mechanical Systems #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2403.06393
openalex publication_date 2024/03/11 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic C0 or C1 continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory of functional connections, and we refer to partitioned domains endowed with these general forms as functionally connected elements (FCE). We further present a method, incorporating functionally connected elements and a least squares collocation approach, for solving boundary and initial value problems. This method exhibits a spectral-like accuracy, with the free functions involved in the FCE form represented by polynomial bases or by non-polynomial bases of quasi-random sinusoidal functions. The FCE method offers a unique advantage over traditional element-based methods for boundary value problems involving relative boundary conditions. A number of linear and nonlinear numerical examples in one and two dimensions are presented to demonstrate the performance of the FCE method developed herein.