Q1. What are the contributions mentioned in the paper "A cartesian grid embedded boundary method for the heat equation on irregular domains" ?
The authors present an algorithm for solving the heat equation on irregular time-dependent domains.
Did you find this useful? Give us your feedback
28 citations
28 citations
26 citations
26 citations
26 citations
...For hyperbolic and parabolic problems, similar ideas have been used [1,25]....
[...]
[...]
40,330 citations
...Similar approaches based on formally inconsistent discretizations at the irregular boundary have been used previously and observed to be stable [1, 9], so we expect that the extension to the more accurate boundary discretization should be straightforward....
[...]
18,443 citations
8,299 citations
...However, it is well known that, for any domain with smooth boundary, a smooth function can be extended to all of R with a bound on the relative increase in the C norms that depends only on the domain and (k; ) [5]....
[...]
1,287 citations
...The method described here, together with that in [6] for elliptic PDEs and [8] for hyperbolic PDEs, provide the fundamental components required for developing second-order accurate methods for a broad range of continuum mechanics problems in irregular geometries based on the predictor–corrector approach in [2]....
[...]
470 citations
...As in previous work on elliptic problems [6], our approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid....
[...]
...We follow the approach described in [6, 7]....
[...]
...With Dirichlet boundary conditions as from (3), we compute an estimate of ∂ψ ∂n by interpolating from the grid values and the values at the boundaries; for details, see [6]....
[...]
...The method described here, together with that in [6] for elliptic PDEs and [8] for hyperbolic PDEs, provide the fundamental components required for developing second-order accurate methods for a broad range of continuum mechanics problems in irregular geometries based on the predictor–corrector approach in [2]....
[...]
...This is routine for the case in which the embedded boundary is contained in the finest level of refinement [6], but requires some additional discretization design when the embedded boundary crosses coarse–fine interfaces....
[...]