Michael Schick

HiFlow 3 : A Hardware-Aware Parallel Finite Element Package

The goal of this paper is to describe the hardware-aware parallel C++ finite element package HiFlow3. HiFlow3 aims at providing a powerful platform for simulating processes modelled by partial differential equations. Our vision is to solve boundary value problems in an appropriate way by coupling numerical simulations with modern software design and state-of-the-art hardware technologies. The main functionalities for mapping the mathematical model into parallel software are implemented in the three core modules Mesh, DoF/FEM and Linear Algebra (LA). Parallelism is realized on two levels. The modules provide efficient MPI-based distributed data structures to achieve performance on large HPC systems but also on stand-alone workstations. Additionally, the hardware-aware cross-platform approach in the LA module accelerates the solution process by exploiting the computing power from emerging technologies like multi-core CPUs and GPUs. In this context performance evaluation on different hardware-architectures will be demonstrated.

Regionalizing Input Data for Generation and Transmission Expansion Planning Models

To support decision making in the context of restructuring the power system, models are needed which allow for a regional, long-term operation and expansion planning for electricity generation and transmission. Input data for these models are needed in a high spatial and temporal granularity. In this paper, we therefore describe an approach aimed at providing regionalized input data for generation and transmission expansion planning models. We particularly focus on a dynamic assignment of renewable energy sources and electrical load to potential buses of the transmission grid. Following a bottom up approach, we model the existing and potential distributed generation and load at the lowest possible spatial resolution based on various databases and models. Besides large power plants, which are directly connected to the transmission grid, a decentralized grid connection is modeled on the distribution grid level based on Voronoi polygons around the corresponding substations. By simplifying the load flow over the distribution grid to a shortest path problem, we model the feed-in into the transmission grid as a variable, depending on the nearest available transmission grid connection. As a result, the connection to the buses at transmission grid level is kept variable in case of grid expansion measures at substation level.

COMPARISON BETWEEN A POLYNOMIAL CHAOS SURROGATE MODEL AND MARKOV CHAIN MONTE CARLO FOR INVERSE UNCERTAINTY QUANTIFICATION BASED ON AN ELECTRIC DRIVE TEST BENCH

The development of uncertainty quantification schemes has been pushed forward due to the increasing demands for complex physical and computational simulation models. In industrial applications, distributions on model parameters play a crucial role and quantifing them is a big challenge. In this work, a test bench hardware is presented, which is designed to measure the motor characteristic of an electric drive. The special aspect of this setup is that parameter distributions, which in general are unknown, can be defined a priori. The obtained measurements serve as a reference to analyse the convergence of Polynomial Chaos (PC) and Markov Chain Monte Carlo (MCMC) in context of Bayesian inference. Our focus is on analysing the feasibility of the PC approach as a surrogate model to replace the forward model in the Bayesian inference. In comparison to the classical approach, which directly uses the simulation model, we investigate the number of simulations needed to obtain a good estimation of the parameter distribution. In addition we use different orders for the PC expansion to fit the surrogate model. In our benchmark, we show that the PC expansion is able to significantly reduce the computational cost compared to a pure MCMC approach.

Optimal Storage Operation with Model Predictive Control in the German Transmission Grid

In this paper, a model predictive control approach is presented to optimize generator and storage operation in the German transmission grid over time spans of hours to several days. In each optimization, a full AC model with typical OPF constraints such as voltage or line capacity limits is used. With given RES and load profiles, inter-temporal constraints such as generator ramping and storage energy are included. Jacobian and Hessian matrices are provided to the solver to enable a fast problem formulation, but the computational bottleneck still lies in solving the linear Newton step. The deviation in storage operation when comparing the solution over the entire horizon of 96 h against the model predictive control is shown in the German transmission grid. The results show that horizons of around 24 h are sufficient with today’s storage capacity, but must be extended when increasing the latter.

Fluid-Structure Interaction Simulation of an Aortic Phantom with Uncertain Young's Modulus Using the Polynomial Chaos Expansion

To add reliability to numerical simulations, Uncertainty Quantification is considered to be a crucial tool for clinical decision making. This especially holds for risk assessment of cardiovascular surgery, for which threshold parameters computed by numerical simulations are currently being discussed. A corresponding biomechanical model includes blood flow, soft tissue deformation, as well as fluid-structure coupling. Thereby, structural material parameters have a strong impact on the dynamic behavior. In practice, however, particularly the value of the Youngs modulus is rarely known in a precise way, and therefore, it reflects a natural level of uncertainty. In this work we introduce a stochastic model for representing variations in the Youngs modulus and quantify its effect on the wall sheer stress and von Mises stress by means of the Polynomial Chaos method. We demonstrate the use of uncertainty quantification in this context and provide numerical results based on an aortic phantom benchmark model.

A POLYNOMIAL CHAOS METHOD FOR UNCERTAINTY QUANTIFICATION IN BLOOD PUMP SIMULATION

Since the end of last century, ventricular assist devices (blood pumps) became one of the most common therapeutic instruments for the treatment of cardiac insufficiency, more than 23 million people are suffering from heart failure worldwide. To this end, computational fluid dynamics (CFD) is widely used in order to get insight into patient specific blood flow behaviour. Despite the fact that a great number of blood pumps are successfully used in practice, there are still many parameters within the CFD simulation, which face uncertainties due to, for example, variations in manufacturing processes or patient specific data. This makes uncertainty quantification an important tool in classical CFD analysis. We consider the Polynomial Chaos expansion with stochastic Galerkin projection in that context. It provides a powerful mean of computing the propagation of uncertainties at once by solution of one single deterministic, and coupled system. A part of the uncertainties we consider are of geometric type, which model an uncertain angular speed of the rotor segment of the pump. We adapt the Multiple Reference Frame method to map the rotation to a stationary reference system and transfer the geometric uncertainty to the Navier-Stokes equations as additional coriolis and centrifugal forces. We compare numerically a Krylov subspace method with mean based preconditioning against a multilevel Polynomial Chaos method for the solution of the governing equations, and verify our results against deterministic reference computations.

A Newton--Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics

The determination of stable limit-cycles plays an important role in quantifying the characteristics of dynamical systems. In practice, exact knowledge of model parameters is rarely available leading to parameter uncertainties, which can be modeled as an input of random variables. This has the effect that the limit-cycles become stochastic themselves, resulting in almost surely time-periodic solutions with a stochastic period. In this paper we introduce a novel numerical method for the computation of stable stochastic limit-cycles based on the spectral stochastic finite element method using polynomial chaos (PC). We are able to overcome the difficulties of PC regarding its well-known convergence breakdown for long term integration. To this end, we introduce a stochastic time scaling which treats the stochastic period as an additional random variable and controls the phase-drift of the stochastic trajectories, keeping the necessary PC order low. Based on the rescaled governing equations, we aim at determini...