Convection Diffusion equation - Revision history

Jureslak: /* References */

2019-07-09T10:06:42Z

References

← Older revision		Revision as of 10:06, 9 July 2019
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	* Slak, J., Kosec, G.. Detection of heart rate variability from a wearable differential ECG device., MIPRO 2016, 39th International Convention, 2016, Opatija, Croatia, ISSN 1847-3938, pp 450-455.		* Slak, J., Kosec, G.. Detection of heart rate variability from a wearable differential ECG device., MIPRO 2016, 39th International Convention, 2016, Opatija, Croatia, ISSN 1847-3938, pp 450-455.

	'''This list might be incomplete, check also reference on the [[Main Page]].'''		'''This list might be incomplete, check also reference on the [[Medusa \| Main Page]].'''

2018-09-24T11:50:55Z

← Older revision	Revision as of 11:50, 24 September 2018
(No difference)

2018-03-15T14:52:12Z

3D cases

← Older revision		Revision as of 14:52, 15 March 2018
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	First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,		First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
	where sides with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups		where sides with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups
	is shown below.		is shown below. Max error is taken for error measure.

	[[File:pois3d_neu_poiss.png\|500px]]		[[File:pois3d_neu_poiss.png\|500px]]

2018-03-15T14:51:04Z

3D cases

← Older revision		Revision as of 14:51, 15 March 2018
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	First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,		First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
	where ~~sided~~ with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups		where sides with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups
	is shown below.		is shown below.

2018-03-15T14:50:37Z

3D cases

← Older revision		Revision as of 14:50, 15 March 2018
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	First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,		First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
	where sided with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\~~dpar~~{u}{\vec{n}} = 0$. The convergence of MLSM in two different setups		where sided with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups
	is shown below.		is shown below.

2018-03-15T14:50:15Z

3D cases

← Older revision		Revision as of 14:50, 15 March 2018
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	== 3D cases ==		== 3D cases ==

			First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
			where sided with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\dpar{u}{\vec{n}} = 0$. The convergence of MLSM in two different setups
			is shown below.

			[[File:pois3d_neu_poiss.png\|500px]]


	And few more 3D cases that are not part of any serious analysis and were made only for fun.		And few more 3D cases that are not part of any serious analysis and were made only for fun.

2018-03-15T14:42:39Z

3D cases

← Older revision		Revision as of 14:42, 15 March 2018
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	A 3-dimensional example, where a CAD model for aluminium heat sink is		A 3-dimensional example, where a CAD model for aluminium heat sink is
	discretized to obtain the domain description.		discretized to obtain the domain description.
	Heat equation with $\alpha = 9.7 \cdot 10^{-5~~}]{m^2}{s~~}$, with no heat generation, i.e. $q = 0 ~~{W}{m^3}~~$, with Dirichlet boundary conditions		Heat equation with $\alpha = 9.7 \cdot 10^{-5}$, with no heat generation, i.e. $q = 0$, with Dirichlet boundary conditions
	$u = ~~\unit[~~100]{^\circ C}$ on the bottom surface and		$u = 100 ^\circ C$ on the bottom surface and
	$u = ~~\unit[~~20]{^\circ C}$ everywhere else.		$u = 20 ^\circ C$ everywhere else.

	[[File:heat_sink_cad.png\|440px]][[File:heat_sink_sol1.png\|440px]][[File:heat_sink_sol2.png\|175px]]		[[File:heat_sink_cad.png\|440px]][[File:heat_sink_sol1.png\|440px]][[File:heat_sink_sol2.png\|175px]]

2018-02-24T14:22:53Z

3D cases

← Older revision		Revision as of 14:22, 24 February 2018
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	== 3D cases ==		== 3D cases ==

	~~First, a 3-dimensional case on domain $[0, 1]^3$ was tested on $N = 20^3$~~
	~~nodes, making the discretization step $\Delta x = 0.05$. Support size of~~
	~~$n=10$ with $m=10$ Gaussian basis functions was used. Their~~
	~~normalization parameter was $\sigma = 60\Delta x$. A time step of $\Delta~~
	~~t = 10^{-5}$ and an explicit Euler method was used to calculate the solution~~
	~~of to $0.01$ time units.~~



	And few more 3D cases that are not part of any serious analysis and were made only for fun.		And few more 3D cases that are not part of any serious analysis and were made only for fun.

2018-02-24T14:22:37Z

3D cases

← Older revision		Revision as of 14:22, 24 February 2018
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	of to $0.01$ time units.		of to $0.01$ time units.

	~~[[File:diffusion3d.png\|300px]]~~

	And few more 3D cases that are not part of any serious analysis and were made only for fun.		And few more 3D cases that are not part of any serious analysis and were made only for fun.
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	[[File:beef_1.png\|350px]][[File:beef_3.png\|350px]][[File:beef_2.png\|350px]]		[[File:beef_1.png\|350px]][[File:beef_3.png\|350px]][[File:beef_2.png\|350px]]

	And finally, steady state temperature profile of a triceratops		And finally, steady state temperature profile of a triceratops and ... a box.

	[[File:triceratops.jpg\|400px]]		[[File:triceratops.jpg\|400px]][[File:diffusion3d.png\|300px]]

	'''We will add more serious 3D results as soon as we get motivated to prepare them, hopefully with some awesome project'''		'''We will add more serious 3D results as soon as we get motivated to prepare them, hopefully with some awesome project'''

2018-02-24T14:22:03Z

Electrostatics Poisson's equation