Heat equation - Revision history

E6WikiAdmin at 18:12, 22 October 2022

2022-10-22T18:12:23Z

2022-10-22T18:12:12Z

2022-10-22T18:11:35Z

2019-10-02T13:30:45Z

‎Effect of sigma and weight

2019-10-02T13:30:19Z

‎Effect of sigma and weight

2019-10-02T13:30:01Z

‎Weighted Least Squares (WLS)

2019-10-02T13:29:46Z

‎Effect of sigma and weight

2019-10-02T13:29:31Z

‎Heat transfer

2019-10-02T13:29:08Z

‎Effect of sigma and weight

2019-10-02T13:28:38Z

‎Finding steady state

← Older revision		Revision as of 18:12, 22 October 2022
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−	*[https://e6.ijs.si/ParallelAndDistributedSystems/publications/98533123.pdf M. Depolli, J. Slak, G. Kosec; Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs, Computers & Structures, 2022 [DOI: 10.1016/j.compstruc.2022.106773]]
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−	~~</syntaxhighlight>~~
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	Go back to [[Medusa#Examples\|Examples]].		Go back to [[Medusa#Examples\|Examples]].

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 <syntaxhighlight>
-J. Slak, G. Kosec; On generation of node distributions for meshless PDE discretizations, SIAM journal on scientific computing, vol. 41, 2019 [DOI: 10.1137/18M1231456]
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← Older revision		Revision as of 18:11, 22 October 2022
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		+	J. Slak, G. Kosec; On generation of node distributions for meshless PDE discretizations, SIAM journal on scientific computing, vol. 41, 2019 [DOI: 10.1137/18M1231456]
		+	</syntaxhighlight>
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	Go back to [[Medusa#Examples\|Examples]].		Go back to [[Medusa#Examples\|Examples]].

← Older revision		Revision as of 13:30, 2 October 2019
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	[[File:heat_trasfer.png\|600px]]		[[File:heat_trasfer.png\|600px]]
	[[File:heat_trasfer_2.png\|600px]]		[[File:heat_trasfer_2.png\|600px]]
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−	We can expect this to have the same error as the simulation with previous function. We can evaluate this by checking what the maximum value is within the domain. Doing so at different numbers of nodes gives us next graph.
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−	~~[[File:maximum_value.png\|800px]]~~
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−	~~Maximum value does't exceed 1.0, which it shouldn't.~~
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−	~~Go back to [[Medusa#Examples\|Examples]].~~

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 We get the following picture.
-[[File:heat_trasfer.png|800px]]
+[[File:heat_trasfer.png|600px]]
+[[File:heat_trasfer_2.png|600px]]
 We can expect this to have the same error as the simulation with previous function. We can evaluate this by checking what the maximum value is within the domain. Doing so at different numbers of nodes gives us next graph.

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 WLS<Gaussians<Vec2d>, GaussianWeight<Vec2d>, ScaleToClosest> wls({9, 75.0}, 1.0);
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 ==Effect of sigma and weight==

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-[[File:different_sigma_1.png|800px]]
+[[File:different_sigma_1.png|600px]]
-[[File:different_sigma_3.png|800px]]
+[[File:different_sigma_3.png|600px]]
-[[File:different_weights_1.png|800px]]
+[[File:different_weights_1.png|600px]]
-[[File:different_weights_2.png|800px]]
+[[File:different_weights_2.png|600px]]
 Now we use sigma 75 and weight 1.0 to solve heat transfer problem. In this case, we don't have analytical sollution. For our boundary condition, we will set up to 0.0, down to 1.0, right to 0.35 and left to 0.75. For the center hole we will use Neumann boundary conditions. We are solving following equations:

← Older revision		Revision as of 13:28, 2 October 2019
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−	~~==Finding steady state==~~
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−	~~To finish simulation we save values of nodes and compare them after some time steps. Next graph shows us how relative error changes, when we increase number of steps, after which we compare values.~~
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−	~~[[File:ending_conditions.png\|800px]]~~
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−	~~In this graph we can see, that using 8000 time steps is sufficient for the size of our domain, which we will use in further simulations.~~

	==Effect of sigma and weight==		==Effect of sigma and weight==