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The numerical studies of both open and closed fictitious boundaries are considered.
Our strategy is based on typical domain splitting algorithm where the initial mesh is split into parts that are then meshed in parallel while the fictitious boundaries between parts are kept unchanged.
Since the MFS source points placement here is not trivial due to the unknown boundary, we employ an adaptive technique to choose a sub-optimal arrangement of source points on various fictitious boundaries.
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GDP is based on creating an artificial and fictitious boundary, assuming that if you produce what you consume, you do not produce.
Turek, D.C. Wan, L.S. Rivkind, The fictitious boundary method for the implicit treatment of Dirichlet boundary conditions with applications to incompressible flow simulations.
In this paper, we investigate the numerical simulation of particulate flows using a new moving mesh method combined with the multigrid fictitious boundary method (FBM) [S.
A correction to the Cauchy Born rule is introduced in the overlap region to minimize fictitious boundary effects.
Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS).
The rectangular domain is assumed to be embedded within a larger circular domain with fictitious boundary loading represented by truncated Fourier series.
An implicit fictitious boundary method (FBM) over a fixed Cartesian grid is extended to model the heat transfer and the phase change in particulate flows in two dimensions.
In order to avoid the occurrence of oscillating boundaries in the optimal design trials, we generate the respective design updates through solving a series of fictitious boundary value problems on an updated Lagrangian configuration.
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