# Efficient computation of basic sums for random polydispersed composites

## Abstract

The main goal of the paper was to develop algorithms and methods for computation of basic sums, the mathematical objects of great importance in computational materials science having applications to description of the representative volume element (RVE) and to the effective properties of 2D composites. The previously used algorithm had the exponential complexity. We propose a linearly complex algorithm. All the presented algorithms can be easily implemented in modern scientific computing packages, while maintaining both efficient calculations and a high level of abstraction. The proposed approach is applied to derivation of a polynomial approximation of the effective conductivity formula for 2D random material with non-overlapping circular inclusions with normally distributed radii. The obtained formulas are applied to the optimal packing problem of disks on the plane.

- Authors:

- Pedagogical University of Cracow, Institute of Computer Science (Poland)

- Publication Date:

- OSTI Identifier:
- 22769314

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; POLYNOMIALS; RANDOMNESS

### Citation Formats

```
Nawalaniec, Wojciech.
```*Efficient computation of basic sums for random polydispersed composites*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0449-6.

```
Nawalaniec, Wojciech.
```*Efficient computation of basic sums for random polydispersed composites*. United States. doi:10.1007/S40314-017-0449-6.

```
Nawalaniec, Wojciech. Tue .
"Efficient computation of basic sums for random polydispersed composites". United States. doi:10.1007/S40314-017-0449-6.
```

```
@article{osti_22769314,
```

title = {Efficient computation of basic sums for random polydispersed composites},

author = {Nawalaniec, Wojciech},

abstractNote = {The main goal of the paper was to develop algorithms and methods for computation of basic sums, the mathematical objects of great importance in computational materials science having applications to description of the representative volume element (RVE) and to the effective properties of 2D composites. The previously used algorithm had the exponential complexity. We propose a linearly complex algorithm. All the presented algorithms can be easily implemented in modern scientific computing packages, while maintaining both efficient calculations and a high level of abstraction. The proposed approach is applied to derivation of a polynomial approximation of the effective conductivity formula for 2D random material with non-overlapping circular inclusions with normally distributed radii. The obtained formulas are applied to the optimal packing problem of disks on the plane.},

doi = {10.1007/S40314-017-0449-6},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}