Basic Ideas.- Systematic Descriptions.- Advanced Approaches.- Convergent Series For Divergent Taylor Series.- Nonlinear Initial Value Problems.- Nonlinear Eigenvalue Problems.- Nonlinear Problems In Heat Transfer.- Nonlinear Problems With Free Or Moving Boundary.- Steady-State Similarity Boundary-Layer Flows.- Unsteady Similarity Boundary-Layer Flows.- Non-Similarity Boundary-Layer Flows.- Applications In Numerical Methods.

Homotopy Analysis Method in Nonlinear Differential Equations

http://numericaltank.sjtu.edu.cn/KeyArticles/LIAO-Notes-2009.pdf

Notes on the homotopy analysis method: Some definitions and theorems

http://numericaltank.sjtu.edu.cn/1stBook/paper/Liao_CNSNS_2009.pdf

An optimal homotopy-analysis approach for strongly nonlinear differential equations

Note: [255] Reference LCH-CONF-1998-009 Record created on 2007-04-24, modified on 2016-08-08

The scaled boundary finite-element method – a primer: derivations

http://www.naoe.eng.osaka-u.ac.jp/naoe/naoe1/image/Reference03.pdf

Review of hydroelasticity theories for global response of marine structures

Short-crested wave interaction with a concentric porous cylindrical structure

Nonlinear progressive waves in water of finite depth — an analytic approximation

7 The scaled boundary ﬁnite-element method (SBFEM) is a novel semi-analytical method 8 developed in the elasto-statics and elasto-dynamics areas that has the advantages of com- 9 bining the ﬁnite-element method with the boundary-element method. The SBFEM method 10 weakens the governing differential equation in the circumferential direction and solves the 11 weakened equation analytically in the radial direction. It has the inherent advantage of 12 solving the unbounded ﬂuid dynamic problem. In this paper, the boundary-value problem 13 composed of short-crested waves diffracted by a vertical circular cylinder is solved by 14 SBFEM. Only the cylinder boundary is discretized with curved surface ﬁnite-elements on 15 the circumference of the cylinder, while the radial differential equation is solved completely 16 analytically. The computation of the diffraction force based on the present SBFEM solu- 17 tion demonstrates a high accuracy achieved with a small number of surface ﬁnite-elements.

Scaled boundary FEM solution of short-crested wave

Scaled boundary FEM solution of short-crested wave diffraction by a vertical cylinder

This paper describes the development of an efficient scaled boundary finite-element model (FEM) for the simulation of short-crested wave interaction with a concentric porous cylindrical structure. By weakening the governing differential equation in the circumferential direction, the SBFEM is able to solve analytically the weakened equation in the radial direction. Only the cylinder boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements, while a complete analytical representation is obtained for the radial differential equation. Comparisons of the numerical results on wave diffraction forces and surface wave elevations at the cylinder to available analytical solutions demonstrate that excellent accuracy can be achieved by the SBFEM with a very small number of surface finite elements. The influence of varying the wave parameters as well as the system configuration on the system hydrodynamics, including the wave force, wave run-up, and diffracted wave contour is examined and extensive results on them are presented. This parametric study will help determine the various hydrodynamic effects of a concentric porous cylindrical structure.

/pdf/scaled-boundary-fem-model-for-interaction-of-short-crested-4z86cwf0a2.pdf

Hao Song

Papers

Short-crested wave interaction with a concentric porous cylindrical structure

Nonlinear progressive waves in water of finite depth — an analytic approximation

Scaled boundary FEM solution of short-crested wave

Scaled boundary FEM solution of short-crested wave diffraction by a vertical cylinder

Scaled Boundary FEM Model for Interaction of Short-Crested Waves with a Concentric Porous Cylindrical Structure