【摘 要】
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We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimization-based shrinking dimer(HiOSD)method for gradient sy
【机 构】
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School of Mathematical Sciences,Peking University,Beijing 100871,China;Beijing International Center
论文部分内容阅读
We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimization-based shrinking dimer(HiOSD)method for gradient systems,a generalized high-index saddle dynamics(GHiSD)is proposed to compute any-index saddles of dynamical systems.Linear stability of the index-k saddle point can be proved for the GHiSD system.A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape,which not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses,but also reveals the relationships between different solutions.Numerical examples,including a three-dimensional example and the phase field model,demonstrate the novel concept of the solution landscape by showing the connected pathway maps.
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