Mathias J. Krause

Towards a hybrid parallelization of lattice Boltzmann methods

Ongoing research towards the development of a hybrid parallelization concept for lattice Boltzmann methods is presented. It allows coping with platforms sharing both the properties of shared and distributed architectures. The proposed approach relies on spatial domain decomposition where each domain represents a basic block entity which is solved on a symmetric multi-processing (SMP) system. Emphasis is placed on the software design and the reworking needed to achieve good performance using OpenMP in that context. Those ideas are implemented in the C++ project OpenLB, which is also sketched in this article. The efficiency of the proposed approaches is tested on a 3D benchmark problem and compared with a purely MPI based approach.

Adjoint-based fluid flow control and optimisation with lattice Boltzmann methods

A lattice Boltzmann (LB) framework to solve fluid flow control and optimisation problems numerically is presented. Problems are formulated on a mesoscopic basis. In a side condition, the dynamics of a Newtonian fluid is described by a family of simplified Boltzmann-like equations, namely BGK-Boltzmann equations, which are linked to an incompressible Navier-Stokes equation. It is proposed to solve the non-linear optimisation problem by a line search algorithm. The needed derivatives are obtained by deriving the adjoint equations, referred to as adjoint BGK-Boltzmann equations. The primal equations are discretised by standard lattice Boltzmann methods (LBM) while for the adjoint equations a novel discretisation strategy is introduced. The approach follows the main ideas behind LBM and is therefore referred to as adjoint lattice Boltzmann methods (ALBM). The corresponding algorithm retains most of the basic features of LB algorithms. In particular, it enables a highly-efficient parallel implementation and thus solving large-scale fluid flow control and optimisation problems. The overall solution strategy, the derivation of a prototype adjoint BGK-Boltzmann equation, the novel ALBM and its parallel realisation as well as its validation are discussed in detail in this article. Numerical and performance results are presented for a series of steady-state distributed control problems with up to approximately 1.6 million unknown control parameters obtained on a high performance computer with up to 256 processing units.

Optimized hybrid parallel lattice boltzmann fluid flow simulations on complex geometries

Computational fluid dynamics (CFD) have become more and more important in the last decades, accelerating research in many different areas for a variety of applications. In this paper, we present an optimized hybrid parallelization strategy capable of solving large-scale fluid flow problems on complex computational domains. The approach relies on the combination of lattice Boltzmann methods (LBM) for the fluid flow simulation, octree data structures for a sparse block-wise representation and decomposition of the geometry as well as graph partitioning methods optimizing load balance and communication costs. The approach is realized in the framework of the open source library OpenLB and evaluated for the simulation of respiration in a subpart of a human lung. The efficiency gains are discussed by comparing the results of the full optimized approach with those of more simpler ones realized prior.

Hybrid parallel simulations of fluid flows in complex geometries: application to the human lungs

In this paper a hybrid parallel strategy dedicated to the simulations of fluid flows in complex geometries by means of Lattice Boltzmann methods (LBM) is introduced. The approach allows coping with platforms sharing both the properties of shared and distributed architectures and relies on spatial domain decomposition where each subdomain represents a basic block entity which is solved on a symmetric multi-processing (SMP) system. Main emphasis is placed on testing its realization and studying its efficiency on a realistic fluid flow problem with a highly complex geometry. Therefore, as a suitable problem the simulation of the expiration in the human lung, whose functionality is described by a dedicated two-scale model, is considered.

Parameter Estimation of Ion Current Formulations Requires Hybrid Optimization Approach to Be Both Accurate and Reliable

Computational models of cardiac electrophysiology provided insights into arrhythmogenesis and paved the way toward tailored therapies in the last years. To fully leverage in silico models in future research, these models need to be adapted to reflect pathologies, genetic alterations, or pharmacological effects, however. A common approach is to leave the structure of established models unaltered and estimate the values of a set of parameters. Today’s high-throughput patch clamp data acquisition methods require robust, unsupervised algorithms that estimate parameters both accurately and reliably. In this work, two classes of optimization approaches are evaluated: gradient-based trust-region-reflective and derivative-free particle swarm algorithms. Using synthetic input data and different ion current formulations from the Courtemanche et al. electrophysiological model of human atrial myocytes, we show that neither of the two schemes alone succeeds to meet all requirements. Sequential combination of the two algorithms did improve the performance to some extent but not satisfactorily. Thus, we propose a novel hybrid approach coupling the two algorithms in each iteration. This hybrid approach yielded very accurate estimates with minimal dependency on the initial guess using synthetic input data for which a ground truth parameter set exists. When applied to measured data, the hybrid approach yielded the best fit, again with minimal variation. Using the proposed algorithm, a single run is sufficient to estimate the parameters. The degree of superiority over the other investigated algorithms in terms of accuracy and robustness depended on the type of current. In contrast to the non-hybrid approaches, the proposed method proved to be optimal for data of arbitrary signal to noise ratio. The hybrid algorithm proposed in this work provides an important tool to integrate experimental data into computational models both accurately and robustly allowing to assess the often non-intuitive consequences of ion channel-level changes on higher levels of integration.

MRI-based computational hemodynamics in patients with aortic coarctation using the lattice Boltzmann methods: Clinical validation study.

To introduce a scheme based on a recent technique in computational hemodynamics, known as the lattice Boltzmann methods (LBM), to noninvasively measure pressure gradients in patients with a coarctation of the aorta (CoA). To provide evidence on the accuracy of the proposed scheme, the computed pressure drop values are compared against those obtained using the reference standard method of catheterization.

A 3D Lattice Boltzmann method for light simulation in participating media

Abstract In recent years, Lattice Boltzmann methods (LBM) have been extended to solve the radiative transport equation (RTE), which describes radiative transport through absorbing and scattering media. With the present work, a new approach for solving RTE by LBM, referred to as RTLBM, is proposed for D 3 Q 7 grids. Its derivation is strongly linked to the P1-method, which approximates the RTE by a macroscopic diffusion equation with an additional sink term. For the fist time, a comprehensive evaluation of an RTLBM is shown. First of all, it is shown by a Chapman–Enskog expansion, that the proposed RTLB equation solves the corresponding macroscopic target diffusion equation with additional sink term. Based on corresponding analytical solutions, a stringent and extensive numerical error analysis, with focus on grid convergence and grid independence, is presented. An experimental order of convergence of two is observed solving the steady-state diffusion equation with additional sink term.

Three-dimensional protein structure prediction based on memetic algorithms

Abstract Tertiary protein structure prediction is a challenging problem in Structural Bioinformatics and is classified according to the computational complexity theory as a NP-hard problem. In this paper, we proposed a first-principle method that makes use of a priori information about known protein structures to tackle the three-dimensional protein structure prediction problem. We do so by designing a multimodal memetic algorithm that uses an evolutionary approach with a ternary tree-structured population allied to a local search strategy. The method has been developed based on an incremental approach using the combination of promising evolutionary components to address the concerned multimodal problem. Three memetic algorithms focused on the problem are proposed. The first one modifies a basic version of a memetic algorithm by introducing modified global search operators. The second uses a different population structure for the memetic algorithm. And finally, the last algorithm consists of the integration of global operators and multimodal strategies to deal with the inherent multimodality of the protein structure prediction problem. The implementations take advantage of structural knowledge stored in the Protein Data Bank to guide the exploiting and restrict the protein conformational search space. Predicted three-dimensional protein structures were analyzed regarding root mean square deviation and the global distance total score test. Obtained results for the three versions outperformed the basic version of the memetic algorithm. The third algorithm overcomes the results of the previous two, demonstrating the importance of adapting the method to deal with the complexities of the problem. In addition, the achieved results are topologically compatible with the experimental correspondent, confirming the promising performance of our approach.

Simultaneous optimization of gait and design parameters for bipedal robots

A walking bipedal robots energy efficiency depends on its gait as well as its design, whereas design changes affect the optimal gaits. We propose a method to take these interdependencies into account via simultaneous optimization of gait as well as design parameters. The method is applied to a planar robot with hybrid zero dynamics control and a torsion spring between its thighs. Periodic gaits are simulated by means of the hybrid zero dynamics. The implementation of the simultaneous optimization of gait parameters and spring stiffness via sequential quadratic programming is presented. Subsequently, an error analysis is performed to gain good convergence and short computation times of the optimization. The evaluation of gradients is identified as crucial for the algorithms convergence and therefore performed via complex step derivative approximations. The resulting implementation exhibits good convergence behavior and is provided as supplement to this paper. At 2.3 m/s, the simultaneous optimization results in savings in energy expenditure of up to 55%. A consecutive optimization of first gait and then stiffness yields only 11%, demonstrating the advantage of the presented method.

Aortic coarctation simulation based on the lattice boltzmann method: benchmark results

We investigate a patient specific blood flow simulation through a transverse aortic arch with a moderate thoracic aortic coarctation, where particular attention is paid to the blood pressure gradient through the coarctation. The challenge in this context is the complex geometry containing a stenosis, which results in complex flow patterns. The fluid is assumed to be incompressible and Newtonian. Its dynamic is usually described by an Navier-Stokes equation with appropriate boundary conditions. Instead, we modeled the problem mesoscopically by a family of BGK-Boltzmann equations those solutions reaches that of a corresponding Navier-Stokes system in a certain limit. For discretization we take advantage of lattice Boltzmann methods, which are realized within the open-source library OpenLB. A realistic transient flow profile of the cardiac output for a human at rest was used to specify the inflow boundary condition at the aortic root, whereas the outflow at the descending aorta was modeled by a pressure boundary condition. A short introduction to lattice Boltzmann methods is provided and especially the used boundary conditions are introduced in detail. The exact simulation setup is stated and the obtained results are discussed.