Scaled Boundary FEM Solution of Wave Diffraction by a Circular Cylinder

2007 ◽  
Author(s):  
Hao Song ◽  
Longbin Tao
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Wave Diffraction ◽  
Wave Structure ◽  
Boundary Element Methods ◽  
Surface Boundary ◽  
Unbounded Medium ◽  
Matrix Differential

The scaled boundary finite-element method (SBFEM) is a novel semi-analytical approach, with the combined advantages of both finite-element and boundary-element methods. The basic idea behind SBFEM is to discretize the surface boundary by FEM and transform the governing partial differential equations to ordinary differential equations of the radial parameter. The radial differential equation is then solved analytically. It has the inherent advantage for solving problems in unbounded medium with discretization to the interface only. In this paper, SBFEM is applied to solve the wave diffraction by a circular cylinder. The final radial matrix differential equation is solved fully analytically without adoption of any numerical scheme. Comparisons to the previous analytical solutions demonstrate the excellent computation accuracy and efficiency of the present SBFEM approach. It also revealed the great potential of the SBFEM to solve more complex wave-structure interaction problems.

Wave Diffraction by a Harbour With Circular Arc Profile by Scaled Boundary FEM

2010 ◽  
Author(s):  
Longbin Tao ◽  
Hao Song
Keyword(s):  
Finite Element ◽  
Wave Diffraction ◽  
Wave Structure ◽  
Wave Theory ◽  
Boundary Element Methods ◽  
Opening Angle ◽  
Linear Wave ◽  
Computational Accuracy ◽  
Circular Arc ◽  
Wave Angle

In this paper, wave diffraction by a harbour is studied by the scaled boundary finite-element method (SBFEM). The semi-analytical approach, with the combined advantages of both finite-element and boundary-element methods, is based on linear wave theory and is applicable to harbours of circular arc profile. The whole solution domain is divided into one unbounded subdomain and one bounded sub-domain by the profile of the harbour. The effects of the incident wave angle and the opening angle of the harbour are discussed. Discretising only the circumference of the harbour, the current semi-analytical SBFEM model exhibits excellent computational accuracy and efficiency. The technique can be extended to solve more practical wave-structure interaction problems with increased complexity.

A hybrid solver based on the integral equation method and vector finite-element method for 3D controlled-source electromagnetic method modeling

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. E319-E333 ◽  
Author(s):  
Rong Liu ◽  
Rongwen Guo ◽  
Jianxin Liu ◽  
Changying Ma ◽  
Zhenwei Guo
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Integral Equation ◽  
Finite Element ◽  
Differential Equations ◽  
Electric Fields ◽  
Hybrid Method ◽  
Linear Equations ◽  
Integral Equation Method ◽  
Controlled Source

The integral equation method (IEM) and differential equation methods have been widely applied to provide numerical solutions of the electromagnetic (EM) fields caused by inhomogeneity for the controlled-source EM method. IEM has a bounded computational domain and has been well-known for its efficiency, whereas differential equation methods are commonly used for complex geologic models. To use the advantages of the two types of approaches, a hybrid method is developed based on the combination of IEM and the edge-based finite-element method (vector FEM). In the hybrid scheme, Maxwell’s differential equations of the secondary electric fields in the frequency domain are derived for a volume with boundary placed slightly away from the inhomogeneity. The vector FEM is applied to solve Maxwell’s differential equations, and a system of linear equations for the secondary electric fields can be derived by the minimum theorem. The secondary electric fields on the boundary are represented by IEM in terms of the secondary electric fields inside the inhomogeneity. The linear equations from substituting the boundary values into the vector FEM linear equations then can be solved to obtain the secondary electric fields inside the inhomogeneity. The secondary electric fields at receivers are calculated by IEM based on the secondary electric field solutions inside the inhomogeneity. The hybrid algorithm is verified by comparison of simulated results with earlier works on canonical 3D disc models with a high accuracy. Numerical comparisons with two conventional IEMs demonstrate that the hybrid method is more accurate and efficient for high-conductivity contrast media.

Hydroelastic Response of a Circular Plate in Waves Using Scaled Boundary FEM

2009 ◽  
Author(s):  
Hao Song ◽  
Longbin Tao
Keyword(s):  
Finite Element ◽  
Circular Plate ◽  
Wave Structure ◽  
Boundary Element Methods ◽  
Order Partial Differential Equation ◽  
Computational Accuracy ◽  
Complex Wave ◽  
Hydroelastic Response ◽  
Incident Waves ◽  
Wave Structure Interaction

In this paper, the hydroelastic response of a circular plate excited by plane incident waves is studied using the scaled boundary finite-element method (SBFEM), a novel semi-analytical approach with the combined advantages of both finite-element and boundary-element methods. The governing sixth-order partial differential equation is decomposed into three Helmholtz-type equations and solved semi-analytically by matching the boundary conditions at the edge of the plate. Discretising only the circumference of the plate, the current SBFEM model exhibits excellent computational accuracy and efficiency. The technique can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

Scaled Boundary FEM Solution of Wave Diffraction by a Square Caisson

2008 ◽  
Author(s):  
Hao Song ◽  
Longbin Tao
Keyword(s):  
Finite Element Method ◽  
Circular Cylinder ◽  
Wave Diffraction ◽  
Unbounded Domains ◽  
Wave Structure ◽  
Structure Interaction ◽  
Irregular Frequency ◽  
Complex Wave ◽  
Wave Structure Interaction ◽  
Scaled Boundary Finite Element

In this paper, the scaled boundary finite-element method (SBFEM) proposed for interaction of wave and circular cylinder [Tao et al, 2007] is modified and applied to wave diffraction by a vertical square caisson. By introducing a virtual circular cylinder surrounding the square caisson, the whole fluid domain is divided into one unbounded subdomain and four bounded subdomins. The corresponding boundary value problems in bounded and unbounded domains are solved by the SBFEM using different base solutions. Comparisons to the previous BEM solutions demonstrate the excellent computation accuracy and efficiency of the present SBFEM approach, as well as the benefit of not suffering from the difficulties of irregular frequency and singularity problems, which are often encountered by BEM. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

scholarly journals Stability Analysis of Linear Sylvester System of First Order Differential Equations

2020 ◽  
Vol 9 (11) ◽  
pp. 25252-25259
Author(s):  
Kasi Viswanadh V. Kanuri ◽  
SriRam Bhagavathula ◽  
K.N. Murty
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stability Criteria ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
First Order ◽  
Matrix Differential ◽  
First Order Differential Equations

    In this paper, we establish stability criteria of the linear Sylvester system of matrix differential equation using the new concept of bounded solutions and deduce the existence of -bounded solutions as a particular case.

scholarly journals Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Fugen Liu ◽  
Tenghao Zhang ◽  
Daniyal M. Alghazzawi ◽  
Nympha Rita Joseph
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Differential Equations ◽  
Design Theory ◽  
Element Model ◽  
Recognition Algorithm ◽  
Bridge Structure ◽  
Modal Parameter ◽  
Art Design ◽  
The Finite Element Model

Abstract A bridge structure is one of the most expressive forms of art design. The artistic expression of bridge structure combines different concepts of structural design and architectural art design. Finite element differential equations are widely used in bridge art design theory and based on these features, the paper adopts the bridge modal parameter recognition algorithm and uses the finite element model to modify and realise the bridge's artistic design. The simulation results show the feasibility of the author's attempt to use the finite element differential equation as the bridge structure art design carrier. After the finite element differential equation modelling, the bridge art structure correction is highly consistent with the experimental results.

On matrix differential equations with several unbounded delays

2006 ◽  
Vol 17 (4) ◽  
pp. 417-433 ◽  
Author(s):  
J. ĈERMÁK
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Equation ◽  
Matrix Differential Equation ◽  
Continuous Vector ◽  
Asymptotic Bounds ◽  
The Matrix ◽  
Exponentially Stable ◽  
Matrix Differential Equations ◽  
Matrix Differential

The paper focuses on the matrix differential equation \[ \dot y(t)=A(t)y(t)+\sum_{j=1}^{m}B_j(t)y(\tau_j(t))+f(t),\quad t\in I=[t_0,\infty)\vspace*{-3pt} \] with continuous matrices $A$, $B_j$, a continuous vector $f$ and continuous delays $\tau_j$ satisfying $\tau_k\circ\tau_l =\tau_l\circ\tau_k$ on $I$ for any pair $\tau_k,\tau_l$. Assuming that the equation \[ \dot y(t)=A(t)y(t)\] is uniformly exponentially stable, we present some asymptotic bounds of solutions $y$ of the considered delay equation. A system of simultaneous Schröder equations is used to formulate these asymptotic bounds.

A Converse Problem in Matrix Differential Equations

1973 ◽  
Vol 16 (3) ◽  
pp. 401-403
Author(s):  
Warren E. Shreveo
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Matrix Differential Equation ◽  
Converse Problem ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Image Position

Suppose X and F are nxn matrix solutions of the n X n matrix differential equation(1)such that(2)where J is some interval.

Fully-Nonlinear Wave-Current-Body Interaction Analysis by a Harmonic Polynomial Cell (HPC) Method

2013 ◽  
Author(s):  
Yan-Lin Shao ◽  
Odd M. Faltinsen
Keyword(s):  
Circular Cylinder ◽  
Boundary Element ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Interaction Analysis ◽  
Harmonic Polynomial ◽  
Boundary Element Methods ◽  
Fully Nonlinear ◽  
Marine Hydrodynamics ◽  
Body Interaction

In the Ronald W. Yeung Honoring Symposium on Offshore and Ship Hydrodynamics in OMAE2012 hold in Rio de Janeiro, Shao & Faltinsen [1] have proposed a new numerical 2D cell method based on representing the velocity potential in each cell by harmonic polynomials. The method was named the Harmonic Polynomial cell (HPC) method. The method was later extended to 3D to study potential-flow problems in marine hydrodynamics [2]. With the considered number of unknowns that are typical in marine hydrodynamics, the comparisons with some existing boundary element based methods including the Fast Multipole Accelerated Boundary Element Methods showed that the HPC method is very competitive in terms of both accuracy and efficiency. The HPC method has also been applied to study fully-nonlinear wave-body interactions [1, 2], for example, sloshing in tanks, nonlinear waves over different sea-bottom topographies and nonlinear wave diffraction by a bottom-mounted vertical circular cylinder. However, no current effects were considered. In this paper, we study the fully-nonlinear time-domain wave-body interaction considering the current effects. In order to validate and verify the method, a bottom-mounted vertical circular cylinder which has been studied extensively in the literature will first be examined. Comparisons are made with published numerical results and experimental results. As a further application, the HPC method will be used to study multiple bottom-mounted cylinders. An example of the wave diffraction of two bottom-mounted cylinders is also presented.

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