Regional connectivity in modified finite point method.

*(English)*Zbl 1297.65151Summary: In this paper, a concept of regional connectivity has been integrated into the modified finite point method (MFPM) [N. J. Wu and T. K. Tsay, “A robust local polynomial collocation method”, Int. J. Num. Methods Eng. 93, No. 4, 355–375 (2013)] to solve problems with different physical behaviors in adjacent regions. This approach has been employed to improve accuracy in its applications to harbor resonance of the MFPM, which has searched adjacent nodes by relative distance for local collocation. By identifying regional connectivity, only closer nodes within regions of the same regional connectivity with respect to a base point can be included for correct local collocation. In coastal engineering, phenomenon of resonance of harbors with breakwaters is a crucial consideration in harbor planning and design. Numerical computations of harbor resonance induced by monochromatic water-waves are used to verify the MFPM numerical model integrated with regional connectivity approach. The whole computational domain is divided into several subdomains, based on different physical behaviors. After numbering of each subdomain, regional connectivity is provided to exclude searching the nearest nodes from inappropriate subdomains for local collocation.

Harbors of different physical geometries, with and without breakwaters have been examined when analytical solutions [C. C. Mei and R. V. Petroni, “Wave in a harbor with protruding breakwaters”, J. Waterw. Harb. Coast. Eng. Div. ASCE 99, No. 2, 209–229 (1973)] are available. Very good agreement between numerical results and analytical solutions has demonstrated that the concept of regional connectivity has improved the performance of MFPM. Application of this regional connectivity concept will be needed in similar problems, such as a crack in a thin plate, and a cutoff of groundwater seepage.

Harbors of different physical geometries, with and without breakwaters have been examined when analytical solutions [C. C. Mei and R. V. Petroni, “Wave in a harbor with protruding breakwaters”, J. Waterw. Harb. Coast. Eng. Div. ASCE 99, No. 2, 209–229 (1973)] are available. Very good agreement between numerical results and analytical solutions has demonstrated that the concept of regional connectivity has improved the performance of MFPM. Application of this regional connectivity concept will be needed in similar problems, such as a crack in a thin plate, and a cutoff of groundwater seepage.

##### MSC:

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

86-08 | Computational methods for problems pertaining to geophysics |

86A20 | Potentials, prospecting |

76S05 | Flows in porous media; filtration; seepage |

##### Keywords:

regional connectivity; harbor resonance; mild-slope equation; mesh-less method; modified finite point method; local polynomial approximation; amplification factor##### Software:

RIDE
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\textit{B. S. Chen} et al., Eng. Anal. Bound. Elem. 47, 21--31 (2014; Zbl 1297.65151)

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