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Numerical simulation of microfluidics on complex surfaces holds significant industrial and scientific value. However, existing numerical methods still face challenges in terms of both physical consistency and computational efficiency. This paper proposes a physically rigorous, computationally robust, and efficient smoothed particle hydrodynamics (SPH) framework. Specifically, we introduce a nonlocal representation of attractive and repulsive forces...

In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid convergence. However, using a large block size also increases the computational cost. Traditionally, the block size is typically reduced after convergence of...