# Scalability of methods to calculate the electrostatic potentials created by charge distributions

#### PRACE

*Status: finished project*

**Contract Number:**

*2010PA0660*

**Starting date**

**Ending date**

The calculation of the electrostatic potential created by a charge distribution is a problem which appears in many fields of both Physics and Chemistry. There exist several popular methods to tackle it.

The recent development of computing facilities made the parallelization features of codes and algorithms critical for their usefulness. The future of cluster computation will probably carry execution of programs in thousands and hundreds of thousands of processors. This new paradigm can have a major influence on the relative properties of standard algorithms. Some methods which hitherto were very popular may not have good scaling properties with such high numbers of processors, and the converse. Moreover, highly parallelizable methods to calculate electrostatic potentials, like the Parallel Fast Fourier Transform or modern versions of the Fast Multipole Method, have recently been developped, and their performance in different HPC architectures must be measured.

Therefore, we propose a project consisting in the comparison of the performance of different methods to calculate electrostatic potentials created by charge distributions. Our aim is to gauge this performance by using the accuracy and the efficiency as a function of the number of processors involved in the simulations. We will compare popular solvers like the conjugate gradients, interpolating scaling functions, multigrid methods, parallel and serial fast Fourier transforms and fast multipole methods.

### Objectives

In our calculations we will use the Octopus code, a quantum chemistry and spectroscopy code mostly based on Density Functional Theory (DFT) and Time-dependent Density Functional Theory (TDDFT). We will perform three different kinds of calculations (if the resources are enough):

1) To calculate the electrostatic potential created by Gaussian charge distributions, whose analytical solutions are known.

2) To calculate the ground state properties of molecular systems using DFT

3) To calculate optical properties based on linear response of molecular systems using DFT and TDDFT

For all three cases, we will measure the accuracy of methods by using known observable quantities, calculated either analytically or with a higher accuracy method. We will also measure the efficiency of the different methods by measuring the execution time required for the calculation of the electrostatic potentials, as a function of the number of processors used (this scaling measurement is actually the most important part of the project).

### Participants

Joseba Alberdi-Rodriguez

Pablo García-Risueño

Angel Rubio

Xavier Andrade

Javier Muguerza

Agustin Arruabarrena