TY - JOUR AB - Purpose The purpose of this paper is to propose an efficient space-time operator-splitting method for the high-dimensional vector-valued Allen–Cahn (AC) equations. The key of the space-time operator-splitting is to devide the complex partial differential equations into simple heat equations and nolinear ordinary differential equations.Design/methodology/approach Each component of high-dimensional heat equations is split into a series of one-dimensional heat equations in different spatial directions. The nonlinear ordinary differential equations are solved by a stabilized semi-implicit scheme to preserve the upper bound of the solution. The algorithm greatly reduces the computational complexity and storage requirement.Findings The theoretical analyses of stability in terms of upper bound preservation and mass conservation are shown. The numerical results of phase separation, evolution of the total free energy and total mass conservation show the effectiveness and accuracy of the space-time operator-splitting method.Practical implications Extensive 2D/3D numerical tests demonstrated the efficacy and accuracy of the proposed method.Originality/value The space-time operator-splitting method reduces the complexity of the problem and reduces the storage space by turning the high-dimensional problem into a series of 1D problems. We give the theoretical analyses of upper bound preservation and mass conservation for the proposed method. VL - 29 IS - 9 SN - 0961-5539 DO - 10.1108/HFF-01-2019-0076 UR - https://doi.org/10.1108/HFF-01-2019-0076 AU - Sun Yunxia AU - Xiao Xufeng AU - Gao Zhiming AU - Feng Xinlong PY - 2019 Y1 - 2019/01/01 TI - An efficient space-time operator-splitting method for high-dimensional vector-valued Allen–Cahn equations T2 - International Journal of Numerical Methods for Heat & Fluid Flow PB - Emerald Publishing Limited SP - 3437 EP - 3453 Y2 - 2024/03/29 ER -