Difference between revisions of "Positioning of computational nodes"
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Although the meshless methods do not require any topological relations between nodes and even randomly distributed nodes could be used, it is well-known that using regularly distributed nodes leads to more accurate and more stable results. So despite meshless seeming robustness regarding the nodal distribution, a certain effort has to be invested into the positioning of the nodes and following discussion, to some extent, deals with this problem. | Although the meshless methods do not require any topological relations between nodes and even randomly distributed nodes could be used, it is well-known that using regularly distributed nodes leads to more accurate and more stable results. So despite meshless seeming robustness regarding the nodal distribution, a certain effort has to be invested into the positioning of the nodes and following discussion, to some extent, deals with this problem. | ||
| − | In a following discussion we want to form set of algorithms that can cover arbitrary domain in n dimensions with nodes that can be further used to solve systems of PDEs. We start with algorithms for filling the domain with nodes. Second set is denoted to improving the nodal distributions and a last set of algorithms deals with the refinement of the nodal distribution. The algorithms can | + | In a following discussion we want to form set of algorithms that can cover arbitrary domain in n dimensions with nodes that can be further used to solve systems of PDEs. We start with algorithms for filling the domain with nodes. Second set is denoted to improving the nodal distributions and a last set of algorithms deals with the refinement of the nodal distribution. The algorithms can of course be combined. |
== Filling the domain with nodes == | == Filling the domain with nodes == | ||
| − | + | It is our goal to fill arbitrary domain, which we can ask if position $\b{p}$ is in the domain our outside, with nodes following the given target density function. | |
== Relaxation of the nodal distribution == | == Relaxation of the nodal distribution == | ||
Revision as of 20:32, 15 January 2018
Although the meshless methods do not require any topological relations between nodes and even randomly distributed nodes could be used, it is well-known that using regularly distributed nodes leads to more accurate and more stable results. So despite meshless seeming robustness regarding the nodal distribution, a certain effort has to be invested into the positioning of the nodes and following discussion, to some extent, deals with this problem. In a following discussion we want to form set of algorithms that can cover arbitrary domain in n dimensions with nodes that can be further used to solve systems of PDEs. We start with algorithms for filling the domain with nodes. Second set is denoted to improving the nodal distributions and a last set of algorithms deals with the refinement of the nodal distribution. The algorithms can of course be combined.
Filling the domain with nodes
It is our goal to fill arbitrary domain, which we can ask if position $\b{p}$ is in the domain our outside, with nodes following the given target density function.
