Parallel simulation of reinforced concrete sructures using peridynamics

The failure of concrete structures involves many complex mechanisms. Traditional theoretical models are limited to specific problems and are not applicable to many real-life problems. Consequently, design specifications mostly rely on empirical equations derived from laboratory tests at the component level. It is desirable to develop new analysis methods, capable of harnessing material-level test parameters. To overcome limitations and shortcomings of models based on continuum mechanics and fracture mechanics, Stewart Silling introduced the concept of peridynamics in 1998. Similar to molecular dynamics, peridynamic modeling of a physical structure involves simulating interacting particles subjected to an empirical force field. The evolution of interacting particles determines the deformation of the structure at a given time due to the applied boundary condition. As a particle-based model, peridynamics requires the repeated evaluation of many particle interactions which is computationally demanding. However, with todays inexpensive computing hardware, parallel algorithms can be utilized to run such problems on multi-node supercomputers with fast interconnects. However, existing codes tend to be domain-specific with too many built-in physical assumptions. In this work, a novel method for parallelization of any particle-based simulation is presented which is quite general and suitable for simulating diverse physical structures. A scalable parallel code for molecular dynamics and peridynamics simulation, PDQ, is described which implements a novel wall method parallelization algorithm, developed as part of this thesis. PDQ partitions the geometric domain of a problem across multi-nodes while the physics is left open to the user to decide whether to simulate a solvated protein or alloy grain boundary at the atomic scale or to simulate cracking phenomena in concrete via peridynamics. A further extension of PDQ brings more flexibility by allowing the user to define any desired number of degrees of freedom for each particle in a peridynamics simulation. At the end of this thesis, plain, reinforced and prestressed concrete benchmark problems are simulated using PDQ and the results are compared to available design code equations or analytical solutions. This research is a step toward next level of computational modeling of reinforced concrete structures and the revolutionizing of how concrete is analyzed and also how concrete structures are designed.\u2

A spectral scheme for Kohn-Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.Comment: Manuscript submitted (with revisions) to Journal of Computational Physic

Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory (DFT) in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics, and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALBs requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55,296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8,586 atoms is 90 seconds, and the time for a graphene sheet containing 11,520 atoms is 75 seconds.Comment: Submitted to The Journal of Chemical Physic

Parallelization solutions for the YNANO Discontinua Simulations.

PhDIn the context of constant and fast progresses in nano technology, discontinua based computation simulations are becoming increasingly important, especially in the context of virtual experimentations. The efficiency of discontinua based nanoscale simulations are still limited by CPU capacity (the number of simulation particles in the system). It is accepted that parallelization will play an important role in solving this problem. In this thesis, two parallelization approaches have been undertaken to parallelize the YNANO discontinua simulations. The scope of the work includes parallelization of the YNANO using the shared-memory approach OpenMP and the distributed-memory approach MPI, and also includes a novel MR_PB linear contact detection algorithm which can be used under periodic boundary conditions. The developed MPI parallelization solutions are compatible with the MR linear contact detection algorithm used in the sequential YNANO, the developed solutions preserves the linearity of both MR_Sort and MR_Search algorithm. The overall performance and scalability of the parallelization has been studied using nanoscale simulations in fluid dynamics and aerodynamics

Multi-Architecture Monte-Carlo (MC) Simulation of Soft Coarse-Grained Polymeric Materials: SOft coarse grained Monte-carlo Acceleration (SOMA)

Multi-component polymer systems are important for the development of new materials because of their ability to phase-separate or self-assemble into nano-structures. The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction with a soft, coarse-grained polymer model is an established technique to investigate these soft-matter systems. Here we present an im- plementation of this method: SOft coarse grained Monte-carlo Accelera- tion (SOMA). It is suitable to simulate large system sizes with up to billions of particles, yet versatile enough to study properties of different kinds of molecular architectures and interactions. We achieve efficiency of the simulations commissioning accelerators like GPUs on both workstations as well as supercomputers. The implementa- tion remains flexible and maintainable because of the implementation of the scientific programming language enhanced by OpenACC pragmas for the accelerators. We present implementation details and features of the program package, investigate the scalability of our implementation SOMA, and discuss two applications, which cover system sizes that are difficult to reach with other, common particle-based simulation methods

Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to: 1) compute a set of vectors that span the occupied subspace of the Hamiltonian; 2) reduce subspace diagonalization to just partially occupied states; and 3) obtain those states in an efficient, scalable manner via an inner Chebyshev-filter iteration. By reducing the necessary computation to just partially occupied states, and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the Discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 hours (of wall time).Comment: Resubmitted version (version 2

Partitioning a macroscopic system into independent subsystems

We discuss the problem of partitioning a macroscopic system into a collection of independent subsystems. The partitioning of a system into replica-like subsystems is nowadays a subject of major interest in several field of theoretical and applied physics, and the thermodynamic approach currently favoured by practitioners is based on a phenomenological definition of an interface energy associated with the partition, due to a lack of easily computable expressions for a microscopic (i.e.~particle-based) interface energy. In this article, we outline a general approach to derive sharp and computable bounds for the interface free energy in terms of microscopic statistical quantities. We discuss potential applications in nanothermodynamics and outline possible future directions.Comment: This is an author-created, un-copyedited version of an article accepted for publication in JSTA