CAJ | 학술논문

本文将紧致积分因子法应用于弹性弯曲势能下红细胞形变过程的相场模型求解。解决了紧致积分因子法如何应用在曲线坐标下具有交叉导数项方程的问题，并对方程中非线性项空间导数和积分因子设计了多项式近似和精确积分结合的混合算法，很大程度地放松了稳定性条件的限制。方法的正确性和效率由数值实验结果进行了验证。本文针对红细胞考虑了柱坐标系下使用紧致积分因子法求解相场方程，但本文所提出的方法也可推广到一般曲线坐标下。
본문장긴치적분인자법응용우탄성만곡세능하홍세포형변과정적상장모형구해。해결료긴치적분인자법여하응용재곡선좌표하구유교차도수항방정적문제，병대방정중비선성항공간도수화적분인자설계료다항식근사화정학적분결합적혼합산법，흔대정도지방송료은정성조건적한제。방법적정학성화효솔유수치실험결과진행료험증。본문침대홍세포고필료주좌표계하사용긴치적분인자법구해상장방정，단본문소제출적방법야가추엄도일반곡선좌표하。
In this paper, we applied compact integration factor(CIF) method to the phase field bending elasticity model for red blood cell membrane deformation. We proposed a scheme to apply CIF method to equations with cross-derivatives under curvilinear coordinate system. Furthermore, we designed a special hybrid interpolation-integration scheme for the spacial derivative of nonlinear terms in the phase ifeld equation, which can largely relax the stability condition. The correctness and effectiveness of the proposed method are verified by the numerical examples presented. In this work, we focus on solving the phase field equations in cylindrical coordinates for red blood cell, however, the proposed method can be easily extended to general curvilinear coordinates.