1,124 research outputs found
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
We review recent advances in the capabilities of the open source ab initio
Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for
greater efficiency and reproducibility. The auxiliary field QMC (AFQMC)
implementation has been greatly expanded to include k-point symmetries,
tensor-hypercontraction, and accelerated graphical processing unit (GPU)
support. These scaling and memory reductions greatly increase the number of
orbitals that can practically be included in AFQMC calculations, increasing
accuracy. Advances in real space methods include techniques for accurate
computation of band gaps and for systematically improving the nodal surface of
ground state wavefunctions. Results of these calculations can be used to
validate application of more approximate electronic structure methods including
GW and density functional based techniques. To provide an improved foundation
for these calculations we utilize a new set of correlation-consistent effective
core potentials (pseudopotentials) that are more accurate than previous sets;
these can also be applied in quantum-chemical and other many-body applications,
not only QMC. These advances increase the efficiency, accuracy, and range of
properties that can be studied in both molecules and materials with QMC and
QMCPACK
Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics
(SEASD), a novel computational method for dynamic simulations of polydisperse
colloidal suspensions with full hydrodynamic interactions. SEASD is based on
the framework of Stokesian Dynamics (SD) with extension to compressible
solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J.
Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet
the performance requirement of dynamic simulations, we use Graphic Processing
Units (GPU) to evaluate the suspension mobility, and achieve an order of
magnitude speedup compared to a CPU implementation. For further speedup, we
develop a novel far-field block-diagonal preconditioner to reduce the far-field
evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of
the mean-field Brownian approximation of Banchio & Brady [J. Chem. Phys. 118
(2003) 10323]. We extensively discuss implementation and parameter selection
strategies in SEASD, and demonstrate the spectral accuracy in the mobility
evaluation and the overall computation scaling. We
present three computational examples to further validate SEASD and SEASD-nf in
monodisperse and bidisperse suspensions: the short-time transport properties,
the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear
Brownian rheology. Our validation results show that the agreement between SEASD
and SEASD-nf is satisfactory over a wide range of parameters, and also provide
significant insight into the dynamics of polydisperse colloidal suspensions.Comment: 39 pages, 21 figure
Numerical simulation of an extensible capsule using regularized Stokes kernels and overset finite differences
In this paper, we present a novel numerical scheme for simulating deformable
and extensible capsules suspended in a Stokesian fluid. The main feature of our
scheme is a partition-of-unity (POU) based representation of the surface that
enables asymptotically faster computations compared to spherical-harmonics
based representations. We use a boundary integral equation formulation to
represent and discretize hydrodynamic interactions. The boundary integrals are
weakly singular. We use the quadrature scheme based on the regularized Stokes
kernels. We also use partition-of unity based finite differences that are
required for the computational of interfacial forces. Given an N-point surface
discretization, our numerical scheme has fourth-order accuracy and O(N)
asymptotic complexity, which is an improvement over the O(N^2 log(N))
complexity of a spherical harmonics based spectral scheme that uses
product-rule quadratures. We use GPU acceleration and demonstrate the ability
of our code to simulate the complex shapes with high resolution. We study
capsules that resist shear and tension and their dynamics in shear and
Poiseuille flows. We demonstrate the convergence of the scheme and compare with
the state of the art
An exact general remeshing scheme applied to physically conservative voxelization
We present an exact general remeshing scheme to compute analytic integrals of
polynomial functions over the intersections between convex polyhedral cells of
old and new meshes. In physics applications this allows one to ensure global
mass, momentum, and energy conservation while applying higher-order polynomial
interpolation. We elaborate on applications of our algorithm arising in the
analysis of cosmological N-body data, computer graphics, and continuum
mechanics problems.
We focus on the particular case of remeshing tetrahedral cells onto a
Cartesian grid such that the volume integral of the polynomial density function
given on the input mesh is guaranteed to equal the corresponding integral over
the output mesh. We refer to this as "physically conservative voxelization".
At the core of our method is an algorithm for intersecting two convex
polyhedra by successively clipping one against the faces of the other. This
algorithm is an implementation of the ideas presented abstractly by Sugihara
(1994), who suggests using the planar graph representations of convex polyhedra
to ensure topological consistency of the output. This makes our implementation
robust to geometric degeneracy in the input. We employ a simplicial
decomposition to calculate moment integrals up to quadratic order over the
resulting intersection domain.
We also address practical issues arising in a software implementation,
including numerical stability in geometric calculations, management of
cancellation errors, and extension to two dimensions. In a comparison to recent
work, we show substantial performance gains. We provide a C implementation
intended to be a fast, accurate, and robust tool for geometric calculations on
polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3
Efficient Fast Multipole Accelerated Boundary Elements via Recursive Computation of Multipole Expansions of Integrals
In boundary element methods (BEM) in , matrix elements and
right hand sides are typically computed via analytical or numerical quadrature
of the layer potential multiplied by some function over line, triangle and
tetrahedral volume elements. When the problem size gets large, the resulting
linear systems are often solved iteratively via Krylov subspace methods, with
fast multipole methods (FMM) used to accelerate the matrix vector products
needed. When FMM acceleration is used, most entries of the matrix never need be
computed explicitly - {\em they are only needed in terms of their contribution
to the multipole expansion coefficients.} We propose a new fast method for the
analytical generation of the multipole expansion coefficients produced by the
integral expressions for single and double layers on surface triangles; charge
distributions over line segments and over tetrahedra in the volume; so that the
overall method is well integrated into the FMM, with controlled error. The
method is based on the per moment cost recursive computation of the
moments. The method is developed for boundary element methods involving the
Laplace Green's function in . The derived recursions are first
compared against classical quadrature algorithms, and then integrated into FMM
accelerated boundary element and vortex element methods. Numerical tests are
presented and discussed.Comment: 6 figures, preprin
An Efficient Framework For Fast Computer Aided Design of Microwave Circuits Based on the Higher-Order 3D Finite-Element Method
In this paper, an efficient computational framework for the full-wave design by optimization of complex microwave passive devices, such as antennas, filters, and multiplexers, is described. The framework consists of a computational engine, a 3D object modeler, and a graphical user interface. The computational engine, which is based on a finite element method with curvilinear higher-order tetrahedral elements, is coupled with built-in or external gradient-based optimization procedures. For speed, a model order reduction technique is used and the gradient computation is achieved by perturbation with geometry deformation, processed on the level of the individual mesh nodes. To maximize performance, the framework is targeted to multicore CPU architectures and its extended version can also use multiple GPUs. To illustrate the accuracy and high efficiency of the framework, we provide examples of simulations of a dielectric resonator antenna and full-wave design by optimization of two diplexers involving tens of unknowns, and show that the design can be completed within the duration of a few simulations using industry-standard FEM solvers. The accuracy of the design is confirmed by measurements
- …