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This paper proposes a strategy to solve the problems of the conventional
s-version of finite element method (SFEM) fundamentally. Because SFEM can
reasonably model an analytical domain by superimposing meshes with different
spatial resolutions, it has intrinsic advantages of local high accuracy, low
computation time, and simple meshing procedure. However, it has disadvantages
such as accuracy of numerical integration and matrix singularity. Although
several additional techniques have been proposed to mitigate these limitations,
they are computationally expensive or ad-hoc, and detract from its strengths.
To solve these issues, we propose a novel strategy called B-spline based SFEM.
To improve the accuracy of numerical integration, we employed cubic B-spline
basis functions with $C^2$-continuity across element boundaries as the global
basis functions. To avoid matrix singularity, we applied different basis
functions to different meshes. Specifically, we employed the Lagrange basis
functions as local basis functions. The numerical results indicate that using
the proposed method, numerical integration can be calculated with sufficient
accuracy without any additional techniques used in conventional SFEM.
Furthermore, the proposed method avoids matrix singularity and is superior to
conventional methods in terms of convergence for solving linear equations.
Therefore, the proposed method has the potential to reduce computation time
while maintaining a comparable accuracy to conventional SFEM.