In recent years, individual-based/agent-based modeling has been applied tostudy a wide range of applications, ranging from engineering problems tophenomena in sociology, economics and biology. Simulating such agent-basedmodels over extended spatiotemporal domains can be prohibitively expensive dueto stochasticity and the presence of multiple scales. Nevertheless, manyagent-based problems exhibit smooth behavior in space and time on a macroscopicscale, suggesting that a useful coarse-grained continuum model could beobtained. For such problems, the equation-free framework [16-18] cansignificantly reduce the computational cost. Patch dynamics is an essentialcomponent of this framework. This scheme is designed to perform numericalsimulations of an unavailable macroscopic equation on macroscopic time andlength scales; it uses appropriately initialized simulations of the fine-scaleagent-based model in a number of small "patches", which cover only a fractionof the spatiotemporal domain. In this work, we construct afinite-volume-inspired conservative patch dynamics scheme and apply it to afinancial market agent-based model based on the work of Omurtag and Sirovich[22]. We first apply our patch dynamics scheme to a continuum approximation ofthe agent-based model, to study its performance and analyze its accuracy. Wethen apply the scheme to the agent-based model itself. Our computationalexperiments indicate that here, typically, the patch dynamics-based simulationrequires only 20% of the full agent-based simulation in space, and need occurover only 10% of the temporal domain.
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