Difference between revisions of "Category:Eigenfunction Matching Method"

From WikiWaves
Jump to navigationJump to search
 
(45 intermediate revisions by 2 users not shown)
Line 1: Line 1:
−
= Introduction =
+
{{complete pages}}
 +
 
 +
== Introduction ==
  
 
A method for solving wave scattering problems in which the solution can be solve
 
A method for solving wave scattering problems in which the solution can be solve
Line 9: Line 11:
 
depth and that there are suitable conditions that we can separate variables. For each problem considered,
 
depth and that there are suitable conditions that we can separate variables. For each problem considered,
 
the simplest case is the semi-infinite domain on one side and open water on the other, and it is this problem
 
the simplest case is the semi-infinite domain on one side and open water on the other, and it is this problem
−
that we focus on in particular. The problem can then be extended to a finite domain, using [[Symmetry in Two Dimension]]
+
that we focus on in particular. The problem can then be extended to a finite domain, using [[:Category:Symmetry in Two Dimensions|Symmetry in Two Dimensions]]
 
and the problem can also be  
 
and the problem can also be  
 
extended to circular regions in three-dimensions.  
 
extended to circular regions in three-dimensions.  
  
−
The method is also called the mode matching method.  
+
The method is also called the mode matching method.
  
−
= Problems for which we have solution =  
+
== Typical Problems ==
  
−
There is no end to the problem which an be solved by this method, and we try to present here the solutions for some of  
+
There is no end to the problems which an be solved by this method, and we try to present here the solutions for some of  
 
the typical problems. As stated previously, we begin with the semi-infinite problem with open water on the left and waves
 
the typical problems. As stated previously, we begin with the semi-infinite problem with open water on the left and waves
−
incident from the left and extend this problem to the finite depth problem by [[Symmetry in Two Dimension]] and
+
incident from the left and extend this problem to the finite depth problem by [[:Category:Symmetry in Two Dimensions|Symmetry in Two Dimensions]] and
 
to the circular problem.  
 
to the circular problem.  
  
−
== Dock ==
+
=== Dock ===
 +
 
 +
[[Image:semiinfinite_dock.jpg|thumb|right|200px|Wave scattering by a semi-infinite dock]]
  
 
The semi-infinite problem is shown on the right.  
 
The semi-infinite problem is shown on the right.  
  
−
[[Image:semiinfinite_dock.jpg|thumb|right|300px|Wave scattering by a semi-infinite dock]]
+
We have the following solutions for this case.
 +
 
 +
* [[Eigenfunction Matching for a Semi-Infinite Dock]]
 +
* [[Eigenfunction Matching for a Finite Dock]]
 +
* [[Eigenfunction Matching for a Finite Dock using Symmetry]]
 +
* [[Two Identical Docks using Symmetry]]
 +
* [[Eigenfunction Matching for a Circular Dock]]
 +
 
 +
=== Submerged Dock ===
 +
 
 +
[[Image:submerged_inf_dock.jpg|thumb|right|200px|Wave scattering by a submerged semi-infinite dock]]
 +
 
 +
The submerged semi-infinite problem is shown on the right.
  
 
We have the following solutions for this case.  
 
We have the following solutions for this case.  
  
−
# [[Eigenfunction Matching for a Semi-Infinite Dock]]
+
* [[Eigenfunction Matching for a Submerged Semi-Infinite Dock]]
−
# [[Eigenfunction Matching for a Circular Dock]]
+
* [[Eigenfunction Matching for a Submerged Finite Dock]]
 +
* [[Two Identical Submerged Docks using Symmetry]]
 +
* [[Eigenfunction Matching for a Submerged Circular Dock]]
 +
 
 +
=== [[:Category:Floating Elastic Plate|Floating Elastic Plate]] ===
 +
 
 +
[[Image:Semiinfinite plate.jpg|thumb|right|200px|Wave scattering by a submerged semi-infinite elastic plate]]
 +
 
 +
The submerged semi-infinite problem is shown on the right.
 +
 
 +
We have the following solutions for this case.
 +
 
 +
* [[Eigenfunction Matching for a Semi-Infinite Floating Elastic Plate]]
 +
* [[Eigenfunction Matching for a Finite Floating Elastic Plate using Symmetry]]
 +
* [[Eigenfunction Matching Method for Floating Elastic Plates]]
 +
* [[Eigenfunction Matching for a Circular Floating Elastic Plate]]
 +
 
 +
=== Submerged Rectangle ===
 +
 
 +
* [[Eigenfunction Matching for a Semi-Infinite Rectangle]]
 +
 
 +
=== Change in Depth ===
 +
 
 +
* [[Eigenfunction Matching for a Semi-Infinite Change in Depth]]
 +
* [[Eigenfunction Matching for a Finite Change in Depth]]
 +
 
 +
=== Vertical Fixed Plate ===
 +
 
 +
* [[Eigenfunction Matching for a Vertical Fixed Plate]]
  
 
[[Category:Linear Water-Wave Theory]]
 
[[Category:Linear Water-Wave Theory]]
 
[[Category:Numerical Methods]]
 
[[Category:Numerical Methods]]

Latest revision as of 12:08, 20 June 2011


Introduction

A method for solving wave scattering problems in which the solution can be solve in various regions using separation of variables. The solution in these regions are then matched at various boundaries. The simplest problem is in Wavemaker Theory, but the separation of variables is also described in Dispersion Relation for a Free Surface

The method is described in Linton and McIver 2001. All that is required is that the domain consists of water of constant depth and that there are suitable conditions that we can separate variables. For each problem considered, the simplest case is the semi-infinite domain on one side and open water on the other, and it is this problem that we focus on in particular. The problem can then be extended to a finite domain, using Symmetry in Two Dimensions and the problem can also be extended to circular regions in three-dimensions.

The method is also called the mode matching method.

Typical Problems

There is no end to the problems which an be solved by this method, and we try to present here the solutions for some of the typical problems. As stated previously, we begin with the semi-infinite problem with open water on the left and waves incident from the left and extend this problem to the finite depth problem by Symmetry in Two Dimensions and to the circular problem.

Dock

Wave scattering by a semi-infinite dock

The semi-infinite problem is shown on the right.

We have the following solutions for this case.

Submerged Dock

Wave scattering by a submerged semi-infinite dock

The submerged semi-infinite problem is shown on the right.

We have the following solutions for this case.

Floating Elastic Plate

Wave scattering by a submerged semi-infinite elastic plate

The submerged semi-infinite problem is shown on the right.

We have the following solutions for this case.

Submerged Rectangle

Change in Depth

Vertical Fixed Plate

Retrieved from "https://wikiwaves.org/wiki/index.php?title=Category:Eigenfunction_Matching_Method&oldid=13185"