Eigenfunction Matching for a Finite Dock using Symmetry - Revision history

Meylan: /* Solution to the original problem */

2010-04-07T02:19:46Z

Solution to the original problem

← Older revision		Revision as of 02:19, 7 April 2010
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	</math>		</math>
	</center>		</center>

	<center>		<center>
	<math>		<math>
	d_{m} = \frac{1}{2}\left(d_{m}^{s}-d_{m}^{a}\right)		d_{m} = \frac{1}{2}\left(a_{m}^{s}-a_{m}^{a}\right)
	</math>		</math>
	</center>		</center>
			Note the formulae for <math>b_m</math> and <math>c_m</math>
			are more complicated but can be derived with some work.

	== Solution with Waves Incident at an Angle ==		== Solution with Waves Incident at an Angle ==

2010-04-07T02:18:17Z

Solution to the original problem

2010-04-07T02:16:41Z

Solution with Waves Incident at an Angle

@@ Line 191: / Line 191: @@
 where we always take the positive real root or the root with positive imaginary part.
-The equations are derived almost identically to those above and we obtain
+The equations are derived almost identically to those above.
 == Matlab Code ==

2010-04-07T02:16:04Z

Solution to the original problem

@@ Line 157: / Line 157: @@
 a_{m} = \frac{1}{2}\left(a_{m}^{s}+a_{m}^{a}\right)
 </math>
 </center>

2010-04-07T02:14:39Z

Matlab Code

@@ Line 174: / Line 174: @@
 </math>.
 </center>
 == Matlab Code ==

2010-04-07T02:14:25Z

Solution with Waves Incident at an Angle

@@ Line 58: / Line 58: @@
 left and right and <math>c_m</math> and <math>d_m</math> are the coefficients under the dock
 covered region. We have an incident wave from the left.
 == Solution using Symmetry ==

2010-04-07T02:14:06Z

Matlab Code

@@ Line 121: / Line 121: @@
 </center>
 and these are solved exactly as before.
 == Solution using Symmetry ==

2010-04-07T02:13:50Z

Numerical Solution

← Older revision		Revision as of 02:13, 7 April 2010
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	left and right and <math>c_m</math> and <math>d_m</math> are the coefficients under the dock		left and right and <math>c_m</math> and <math>d_m</math> are the coefficients under the dock
	covered region. We have an incident wave from the left.		covered region. We have an incident wave from the left.

	~~==Numerical Solution==~~

	~~To solve the system of equations we set the upper limit of <math>l</math> to~~
	~~be <math>M</math>. We then simply need to solve the linear system of equations.~~

	== Solution with Waves Incident at an Angle ==		== Solution with Waves Incident at an Angle ==

2010-04-07T02:13:34Z

An infinite dimensional system of equations

@@ Line 58: / Line 58: @@
 left and right and <math>c_m</math> and <math>d_m</math> are the coefficients under the dock
 covered region. We have an incident wave from the left.
 ==Numerical Solution==

2010-04-07T02:11:59Z

Introduction

← Older revision		Revision as of 02:11, 7 April 2010
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	at an angle. For the later we give the equations in slightly less detail.		at an angle. For the later we give the equations in slightly less detail.
	The theory is based on [[Eigenfunction Matching for a Semi-Infinite Dock]] and this should		The theory is based on [[Eigenfunction Matching for a Semi-Infinite Dock]] and this should
	be consulted for many details~~. The solution here can be straightforwardly extended~~		be consulted for many details.
	~~using [[:Category:Symmetry in Two Dimensions\|Symmetry in Two Dimensions]] to two docks of the same length and this can be~~
	~~found [[Two Identical Docks using Symmetry]]. We also show how the solution~~
	~~can be found using [[:Category:Symmetry in Two Dimensions\|Symmetry in Two Dimensions]] for the finite dock~~.

	==Governing Equations==		==Governing Equations==