Parallel Dynamic Programming for the Exact Computation of Density of State for 2<i>D</i> Spin-Crossover Nanomaterials

We discuss the design, the analysis and the parallel implementation of a dynamic programming approach for the computation of the density of state in the simulation of spin-crossover nanoparticles. The motivation is the computation of a Hamiltonian, which is usually approximated using Monte Carlo techniques. However, physicists need better control of the accuracy of this approximation. An exact counting algorithm allows this error to be controlled, and also measures the impact on accuracy for the entire simulation. We propose an exact parallel counting algorithm and its two-level parallel implementation to tackle nanoscale problems on HPC architecture. We discuss its scalability and feasibility for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>D</mi></mrow></semantics></math></inline-formula> grids of <i>n</i> molecules. The new algorithm enables the exact computation for a three-variable density of state at nanoscale, which is seen as intractable. A comparison between the expectation of the model and implementation is proposed. The parallel complexity achieved is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>5</mn><mn>2</mn></mfrac></mstyle></msup><msup><mn>2</mn><msqrt><mi>n</mi></msqrt></msup><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and the results allow the prediction of never-before-seen phenomena.