A massively parallel solver for discrete Poisson-like problems

Typically, to calculate the two-particle Coulomb interaction between nanostructures, a six dimensional spatial integral need to be evaluated. For increasing size or complexity of the system, the calculation of the Coulomb coupling elements presents a significant limiting factor for simulations. The number of integrals in real space can be reduced by using a Green's function representation of the solution of a generalized Poisson equation. Without the restriction to specific symmetries, this efficient numerical method allows the inclusion of an arbitrary dielectric function.The Coulomb interaction between two colloidal quantum dots (QDs) is calculated without specifying the Green's function to an explicit analytic form. Nevertheless, the monopole-monopole interaction and the Förster induced excitation transfer are calculated separately. The Coulomb coupling between semiconductor QDs depends on the center-to-center distance between the nanostructures as well as on their relative dipole orientation to each other. To identify the effects of the spatially dependent Coulomb coupling on single excitons and biexcitons, a multidimensional coherent spectroscopy is used. The characteristic two dimensional optical signatures of different spatial arranged colloidal QDs are calculated with respect to the arrangement dependent Coulomb coupling between the nanostructures.

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“…(14). 21,22 Therefore, solving the Poisson Eq. (14) and evaluating the three dimensional integral in Eq.…”

Section: Poisson Green's Function Methodsmentioning

confidence: 99%

Efficient numerical method for calculating Coulomb coupling elements and its application to two-dimensional spectroscopy

2016

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“…This approach allows us to reduce of a factor three the number of memory access operations, since the values of the vector w that is involved in all the three products can be maintained in the registers. However, the reordering proposed in [25] requires an additional AXPY computation(the update of a vector Y as Y = αX + Y). We grouped the AXPY computations in two pairs that are executed in a single kernel.…”

Section: Application Of the Preconditionermentioning

confidence: 99%

AMG based on compatible weighted matching for GPUs

Bernaschi¹,

D'Ambra²,

Pasquini

2020

Parallel Computing

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We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic MultiGrid (AMG) preconditioner previously proposed by one of the authors and already available in the open-source package BootCMatch: Bootstrap algebraic multigrid based on Compatible weighted Matching for standard CPU. The AMG method relies on a new approach for coarsening sparse symmetric positive definite (s.p.d.) matrices, named coarsening based on compatible weighted matching. It exploits maximum weight matching in the adjacency graph of the sparse matrix, driven by the principle of compatible relaxation, providing a suitable aggregation of unknowns which goes beyond the limits of the usual heuristics applied in the current methods. We adopt an approximate solution of the maximum weight matching problem, based on a recently proposed parallel algorithm, referred as the Suitor algorithm, and show that it allow us to obtain good quality coarse matrices for our AMG on GPUs. We exploit inherent parallelism of modern GPUs in all the kernels involving sparse matrix computations both for the setup of the preconditioner and for its application in a Krylov solver, outperforming preconditioners available in Nvidia AmgX library. We report results about a large set of linear systems arising from discretization of scalar and vector partial differential equations (PDEs).

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“…They only involve a direct solver at the coarsest level, and intermediate levels are still carried out in an iterative way, thus exhibiting good strong (based on SpMV) and weak scalabilities (multilevel). Convergence is nevertheless problem dependent [49,50].…”

Section: Domain Decomposition Erhel and Giraud Summarized The Attracmentioning

confidence: 99%

High-Performance Computing: Dos and Don’ts

Houzeaux¹,

Borrell²,

Fournier³

et al. 2018

Computational Fluid Dynamics - Basic Instruments and Applications in Science

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Computational fluid dynamics (CFD) is the main field of computational mechanics that has historically benefited from advances in high-performance computing. Highperformance computing involves several techniques to make a simulation efficient and fast, such as distributed memory parallelism, shared memory parallelism, vectorization, memory access optimizations, etc. As an introduction, we present the anatomy of supercomputers, with special emphasis on HPC aspects relevant to CFD. Then, we develop some of the HPC concepts and numerical techniques applied to the complete CFD simulation framework: from preprocess (meshing) to postprocess (visualization) through the simulation itself (assembly and iterative solvers).

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A massively parallel solver for discrete Poisson-like problems

Cited by 38 publications

References 31 publications

Efficient numerical method for calculating Coulomb coupling elements and its application to two-dimensional spectroscopy

Efficient numerical method for calculating Coulomb coupling elements and its application to two-dimensional spectroscopy

AMG based on compatible weighted matching for GPUs

High-Performance Computing: Dos and Don’ts

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