Adaptivity - Revision history

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Mitjajancic: typo

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typo

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 [https://e6.ijs.si/ParallelAndDistributedSystems/publications/32230439.pdf J. Slak, G. Kosec; Adaptive radial basis function-generated finite differences method for contact problems, International journal for numerical methods in engineering, vol. 119, 2019 [DOI: 10.1002/nme.6067]]
 }}
 Solutions to many physical problems governed by partial differential equations (PDE) often significantly vary in magnitude throughout the problem domain. Although in some special cases the areas with high error are known in advance, in general the error distribution is unknown beforehand. Adaptive techniques for solving PDEs are a standard way of dealing with this problem, where problematic regions are iteratively refined. A step further is automatic adaptivity, where problematic regions are chosen automatically using an error indicator and then refined, until certain error threshold is reached. Below, we show some examples of fully automatic adaptivity in Medusa.

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 [https://e6.ijs.si/ParallelAndDistributedSystems/publications/32230439.pdf J. Slak, G. Kosec; Adaptive radial basis function-generated finite differences method for contact problems, International journal for numerical methods in engineering, vol. 119, 2019 [DOI: 10.1002/nme.6067]]
 }}
 Solutions to many physical problems governed by partial differential equations (PDE) often significantly vary in magnitude throughout the problem domain. Although in some special cases the areas with high error are known in advance, in general the error distribution is unknown beforehand. Adaptive techniques for solving PDEs are a standard way of dealing with this problem, where problematic regions are iteratively refined. A step further is automatic adaptivity, where problematic regions are chosen automatically using an error indicator and then refined, until certain error threshold is reached. Below, we show some examples of fully automatic adaptivity in Medusa.
 ==  Basic concept ==

← Older revision		Revision as of 19:26, 22 October 2022
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	Go back to [[Medusa#Examples\|Examples]].		Go back to [[Medusa#Examples\|Examples]].

		+	{{Box-round\|title= Related papers \|
		+	[https://e6.ijs.si/ParallelAndDistributedSystems/publications/32230439.pdf J. Slak, G. Kosec; Adaptive radial basis function-generated finite differences method for contact problems, International journal for numerical methods in engineering, vol. 119, 2019 [DOI: 10.1002/nme.6067]]
		+	}}

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 Go back to [[Medusa#Examples|Examples]].
 Solutions to many physical problems governed by partial differential equations (PDE) often significantly vary in magnitude throughout the problem domain. Although in some special cases the areas with high error are known in advance, in general the error distribution is unknown beforehand. Adaptive techniques for solving PDEs are a standard way of dealing with this problem, where problematic regions are iteratively refined. A step further is automatic adaptivity, where problematic regions are chosen automatically using an error indicator and then refined, until certain error threshold is reached. Below, we show some examples of fully automatic adaptivity in Medusa.
 ==  Basic concept ==

← Older revision		Revision as of 19:26, 22 October 2022
Line 1:		Line 1:
		+	Go back to [[Medusa#Examples\|Examples]].

		+	{{Box-round\|title= Related papers \|
		+	[https://e6.ijs.si/ParallelAndDistributedSystems/publications/32230439.pdf J. Slak, G. Kosec; Adaptive radial basis function-generated finite differences method for contact problems, International journal for numerical methods in engineering, vol. 119, 2019 [DOI: 10.1002/nme.6067]]
		+	}}

−
−	~~Go back to [[Medusa#Examples\|Examples]].~~

	Solutions to many physical problems governed by partial differential equations (PDE) often significantly vary in magnitude throughout the problem domain. Although in some special cases the areas with high error are known in advance, in general the error distribution is unknown beforehand. Adaptive techniques for solving PDEs are a standard way of dealing with this problem, where problematic regions are iteratively refined. A step further is automatic adaptivity, where problematic regions are chosen automatically using an error indicator and then refined, until certain error threshold is reached. Below, we show some examples of fully automatic adaptivity in Medusa.		Solutions to many physical problems governed by partial differential equations (PDE) often significantly vary in magnitude throughout the problem domain. Although in some special cases the areas with high error are known in advance, in general the error distribution is unknown beforehand. Adaptive techniques for solving PDEs are a standard way of dealing with this problem, where problematic regions are iteratively refined. A step further is automatic adaptivity, where problematic regions are chosen automatically using an error indicator and then refined, until certain error threshold is reached. Below, we show some examples of fully automatic adaptivity in Medusa.

← Older revision		Revision as of 19:25, 22 October 2022
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−	~~{{Box-round\|title= Related papers \|~~	+
−	[https://e6.ijs.si/ParallelAndDistributedSystems/publications/32230439.pdf J. Slak, G. Kosec; Adaptive radial basis function-generated finite differences method for contact problems, International journal for numerical methods in engineering, vol. 119, 2019 [DOI: 10.1002/nme.6067]]
−	}}

	Go back to [[Medusa#Examples\|Examples]].		Go back to [[Medusa#Examples\|Examples]].

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 The adaptive methodology in this paper behaves similarly to "remeshing" used commonly in FEM.
-Some initial (possibly variable) nodal spacing $h^0$ is chosen, as well as its lower and upper bounds $h_L$ and  $h_U$, respectively. 3
+Some initial (possibly variable) nodal spacing $h^0$ is chosen, as well as its lower and upper bounds $h_L$ and  $h_U$, respectively.
 Domain $\Omega$ is filled with nodes, conforming to $h^0$ and the solution $u^0$ is obtained.
 An error indicator is employed to determine which nodes should be (de)refined and the nodal density $h^0$ is altered appropriately.