离散化
非线性系统
多边形网格
数学
守恒定律
应用数学
稳健性(进化)
方案(数学)
放松(心理学)
数学分析
物理
几何学
量子力学
心理学
社会心理学
生物化学
化学
基因
作者
Agissilaos Athanassoulis,Theodoros Katsaounis,Irene Kyza,Stephen Metcalfe
标识
DOI:10.1016/j.jcp.2023.112307
摘要
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrödinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach in the spirit of [10], [11], [34] for the nonlinear Schrödinger equation. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system's mass conservation and energy balance laws for constant meshes. The scheme is seen to be second order in time. We conclude by presenting some numerical experiments, including an example from cosmology and an example with variable time-steps which demonstrate the effectiveness and robustness of the new scheme.
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