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math.NA2026
DTPFI: A stable algorithm for recovering nonlinear energy potentials in phase field systems
Tianhao Ni, Jun Lai
This work proposes a Dual Time Phase Field Inversion (DTPFI) method for recovering unknown potential functions in phase field models. The reconstruction is formulated as an optimiz…
math.NA2025
A Singularity Guided Nyström Method for Elastostatics on Two Dimensional Domains with Corners
Baoling Xie, Jun Lai
We develop a comprehensive analytical and numerical framework for boundary integral equations (BIEs) of the 2D Lamé system on cornered domains. By applying local Mellin analysis o…
math.NA2024
Recursive sparse LU decomposition based on nested dissection and low rank approximations
Zhu Xuanru, Lai Jun
When solving partial differential equations (PDEs) using finite difference or finite element methods, efficient solvers are required for handling large sparse linear systems. In th…