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Register a new userA fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
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For embedded boundary electromagnetics using the Dey-Mittra algorithm, a special grad-div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwells curl-curl matrix. Efficient curl-curl
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We present a multigrid scheme for the solution of finite-element Hartree-Fock equations for diatomic molecules. It is shown to be fast and accurate, the time effort depending linearly on the number of variables. Results are given for the molecules LiH, BH, N_2 and for the Be atom in our molecular grid which agrees very well with accurate values from an atomic code. Highest accuracies were obtained by applying an extrapolation scheme; we compare with other numerical methods. For N_2 we get an accuracy below 1 nHartree.
The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the solid-fluid interaction scheme yields very large spurious currents in the simulations involving curved boundaries, while the virtual-density scheme produces an unphysical thick mass-transfer layer near the solid boundary although it gives much smaller spurious currents. We also extend the geometric-formulation scheme in the phase-field method to the pseudopotential LB model. Nevertheless, in comparison with the solid-fluid interaction scheme and the virtual-density scheme, the geometric-formulation scheme is relatively difficult to implement for curved boundaries and cannot be directly applied to three-dimensional space. By analyzing the features of these three schemes, we propose an improved virtual-density scheme to implement contact angles in the pseudopotential LB simulations with curved boundaries, which does not suffer from a thick mass-transfer layer near the solid boundary and retains the advantages of the original virtual-density scheme, i.e., simplicity, easiness for implementation, and low spurious currents.
We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD computations. Since the $gamma_5$-preserving aggregation based interpolation used in our multigrid method is valid for both, the Hermitian and the non-Hermitian case,
We present details of our implementation of the Wuppertal adaptive algebraic multigrid code DD-$alpha$AMG on SIMD architectures, with particular emphasis on the Intel Xeon Phi processor (KNC) used in QPACE 2. As a smoother, the algorithm uses a domain-decomposition-based solver code previously developed for the KNC in Regensburg. We optimized the remaining parts of the multigrid code and conclude that it is a very good target for SIMD architectures. Some of the remaining bottlenecks can be eliminated by vectorizing over multiple test vectors in the setup, which is discussed in the contribution of Daniel Richtmann.
In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows. First, we introduce a fast moving least squares (fast-MLS) approximation technique with which we speed up the process of building transfer functions during the simulations which leads to considerable reductions in computational time. We compare the accuracy of the fast-MLS against the exact moving least squares (MLS) for the standard problem of uniform flow over a sphere. In order to overcome the restrictions set by the resolution coupling of the Lagrangian and Eulerian meshes in this particular immersed boundary method, we present an adaptive Lagrangian mesh refinement procedure that is capable of drastically reducing the number of required nodes of the basic Lagrangian mesh when the immersed boundaries can move and deform. Finally, a coarse-grained collision detection algorithm is presented which can detect collision events between several Lagrangian markers residing on separate complex geometries with minimal computational overhead.
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