Related papers: Fast Numerical Simulation of Allen-Cahn Equation
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The Allen-Cahn equation is a gradient system, where the free-energy functional decreases monotonically in time. We develop an energy stable reduced order model (ROM) for a gradient system, which inherits the energy decreasing property of…
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In this paper, by using Strang's second-order splitting method, the numerical procedure for the three-dimensional (3D) space fractional Allen-Cahn equation can be divided into three steps. The first and third steps involve an ordinary…
Due to decelerating gains in single-core CPU performance, computationally expensive simulations are increasingly executed on highly parallel hardware platforms. Agent-based simulations, where simulated entities act with a certain degree of…
Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…
This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable…
We develop convergence acceleration procedures that enable a gradient descent-type iteration method to efficiently simulate Hartree--Fock equations for atoms interacting both with each other and with an external potential. Our development…
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