Combining the kernel estimate with the Taylor series expansion is proposed to develop a Corrective Smoothed Particle Method (CSPM). This algorithm resolves the general problem of particle deficiency at boundaries, which is a shortcoming in Standard Smoothed Particle Hydrodynamics (SSPH). In addition, the method’s ability to model derivatives of any order could make it applicable for any time‐dependent boundary value problems. An example of the applications studied in this paper is unsteady heat conduction, which is governed by second‐order derivatives. Numerical results demonstrate that besides the capability of directly imposing boundary conditions, the present method enhances the solution accuracy not only near or on the boundary but also inside the domain. Published in 1999 by John Wiley & Sons, Ltd. This article is a U.S. government work and is in the public domain in the United States.

Most of the ultrafast laser heating analysis to date has been accomplished with a constant electron–phonon coupling factor (G). Due to the significant changes in the electron and lattice temperature caused by high-power laser heating, G could be temperature dependent. In this article a phenomenological temperature-dependent G is introduced to simulate ultrafast laser heating in metals. The electron temperature and the ablation depth computed with the temperature-dependent G compare well with experimental data.

A corrective Smoothed-Particle Method (CSPM) is proposed to address the tensile instability and, boundary de®ciency problems that have hampered full exploitation of standard smoothed particle hydrodynamics (SPH). The results from applying this algorithm to the 1-D bar and 2-D plane stress problems are promising. In addition to the advantage of being a gridless Lagrangian approach, improving the above two major obstacles in standard SPH makes it attractive for applications in computational mechanics.

Two different solution algorithms of the corrective smoothed particle method (CSPM) are developed and examined with linear elastodynamic problems. One is to use the corrective ®rst derivative approximations to solve the stress-based momentum equations, with stresses evaluated from the strains. This is an approach that has widely been adopted in smoothed particle hydrodynamics (SPH) methods. The other is new, in which the corrective second derivative approximations are used to directly solve the displacement-based Navier equations. The former satis®es the nodal completeness condition but lacks integrability; on the contrary, the latter is truly complete. Numerical tests show that the latter outperforms the former as well as other existing SPH methods, as expected.

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