# Stellar surface as low-rank modification in iterative methods for binary neutron stars

## Abstract

We present a new multidomain spectral method for the treatment of non-spherical stellar surfaces in iterative methods for binary neutron stars. A stellar surface changes throughout the course of an iterative solution, potentially stalling the convergence. Our method affords low-complexity updates of the relevant subdomain preconditioners, thereby avoiding such stalling. Unlike current collocation (or nodal) approaches for treating surfaces (which rely on coordinate transformations to ensure that stellar surfaces arise at subdomain boundaries), our approach requires no regridding or nontrivial Jacobians. For polytropes with an equation of state specified by an integer polytropic index, our method delivers exponential accuracy with increased truncation, although for “stiff” equations of state (e.g. fractional) it suffers from the same accuracy loss as current methods. We have presented an outline of our approach before, but here present details with numerical tests.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22701621

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 348; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BINARY STARS; EQUATIONS OF STATE; ITERATIVE METHODS; MATHEMATICAL SOLUTIONS; MODIFICATIONS; NEUTRON STARS

### Citation Formats

```
Lau, Stephen R., E-mail: lau@math.unm.edu.
```*Stellar surface as low-rank modification in iterative methods for binary neutron stars*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2017.07.026.

```
Lau, Stephen R., E-mail: lau@math.unm.edu.
```*Stellar surface as low-rank modification in iterative methods for binary neutron stars*. United States. doi:10.1016/J.JCP.2017.07.026.

```
Lau, Stephen R., E-mail: lau@math.unm.edu. Wed .
"Stellar surface as low-rank modification in iterative methods for binary neutron stars". United States. doi:10.1016/J.JCP.2017.07.026.
```

```
@article{osti_22701621,
```

title = {Stellar surface as low-rank modification in iterative methods for binary neutron stars},

author = {Lau, Stephen R., E-mail: lau@math.unm.edu},

abstractNote = {We present a new multidomain spectral method for the treatment of non-spherical stellar surfaces in iterative methods for binary neutron stars. A stellar surface changes throughout the course of an iterative solution, potentially stalling the convergence. Our method affords low-complexity updates of the relevant subdomain preconditioners, thereby avoiding such stalling. Unlike current collocation (or nodal) approaches for treating surfaces (which rely on coordinate transformations to ensure that stellar surfaces arise at subdomain boundaries), our approach requires no regridding or nontrivial Jacobians. For polytropes with an equation of state specified by an integer polytropic index, our method delivers exponential accuracy with increased truncation, although for “stiff” equations of state (e.g. fractional) it suffers from the same accuracy loss as current methods. We have presented an outline of our approach before, but here present details with numerical tests.},

doi = {10.1016/J.JCP.2017.07.026},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 348,

place = {United States},

year = {2017},

month = {11}

}