Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

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• 作者：Markus Weinm&uuml ; ller ; Michael Weinm&uuml ; ller ; Jonathan Rohland ; Armin Scrinzi ; ^{armin.scrinzi@lmu.de}
• 关键词：Absorbing boundary condition ; Finite difference ; Non-equidistant grid ; Finite-element discrete variable representation ; Complex scaling ; Schrö ; dinger equation
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：333
• 期：Complete
• 页码：199-211
• 全文大小：682 K
• 卷排序：333

文摘

Two non-equidistant grid implementations of infinite range exterior complex scaling are introduced that allow for perfect absorption in the time dependent Schrödinger equation. Finite element discrete variables discretizations provide as efficient absorption as the corresponding finite elements discretizations. This finding is at variance with results reported in literature [L. Tao et al., Phys. Rev. A 48, 063419 (2009)]. For finite differences, a new class of generalized Q  -point schemes for non-equidistant grids is derived. Convergence of absorption is exponential ∼ΔxQ−1∼ΔxQ−1 and numerically robust. Local relative errors ≲10−9≲10−9 are achieved in a standard problem of strong-field ionization.