A Multidomain spectral method for solving elliptic equations
By Harald P. Pfeiffer, Lawrence E. Kidder, Mark A. Scheel, Saul A. Teukolsky. 2002
191 citations recorded by the source corpus.
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three distinct features. First, the combined problem of solving the PDE, satisfying the boundary conditions, and matching between different subdomains is cast into one set of equations readily accessible to standard linear and nonlinear solvers. Second, touching as well as overlapping subdomains are supported; both rectangular blocks with Chebyshev basis functions as well as spherical shells with an expansion in spherical harmonics are implemented. Third, the code is very flexible: The domain decomposition as well as the distribution of collocation points in each domain can be chosen at run time, and the solver is easily adaptable to new PDEs. The code has been used to solve the equations of the initial value problem of general relativity and should be useful in many other problems. We compare the new method to finite difference codes and find it superior in both runtime and accuracy, at least for the smooth problems considered here.
Subfields: Computational Mechanics, Mechanics of Materials, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/922b411042d1328f55a97ebade429867c57a8ff7
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In Numerical Analysis
- Harald P. Pfeiffer
- J. V. Meter
- B. Kelly
- John G. Baker
- J. Centrella
- Mark A. Scheel
- Lawrence E. Kidder
Citations in the corpus
- Black-hole binaries, gravitational waves, and numerical relativity (2010, methodology): “is tools used by many groups; • modern adaptive mesh refinement finite-difference (including Carpet2 with Cactus, BAM (Bru¨gmann, 1999), and Paramesh (MacNeice et al., 2000)), and multi-domain spectral (Pfeiffer et al., 2003) infrastructures for numerical relativity. Throughout this period, the length o”
- Surrogate model of hybridized numerical relativity binary black hole waveforms (2018, methodology): “The NR simulations for this model are performed using the Spectral Einstein Code (SpEC) [51–56] developed by the SXS [57] collaboration.”