Radial basis function interpolation for black-box multi-physics simulations

Interpolation based on radial basis functions (RBF) is a standard data map- ping method used in multi-physics coupling. It works on scattered data without requiring additional mesh topology or neighborhood information of support points. However, sys- tem matrices of the equations for the coefficients tend to be ill-conditioned. In this work, we illustrate the problem by a simple example and discuss possible remedies. Furthermore, we investigate the numerical performance of this method on uniform and non-uniform meshes with a particular focus on the coupling of black-box components where typically no information about the underlying discretization can be extracted. Radial basis func- tion interpolation usually uses an enhancement of the radial basis functions by a global polynomial in order to properly capture constant components and linear trends in the given data. We present a method that determines this polynomial independent from the radial basis function ansatz, which substantially improves the condition number of the remaining RBF system. Furthermore, we show that a rescaling approach can be used to either increase the accuracy or improve the condition number even further by choosing radial basis functions with a smaller support radius. The results represent an intermediate state with the aim to be integrated into the multi-physics coupling library preCICE

A Simple Test Case for Convergence Order in Time and Energy Conservation of Black-Box Coupling Schemes

The most commonly used coupling schemes in partitioned multiphysics simulations suffer from a decrease in the order of convergence, specifically in the time domain; a phenomenon we call order degradation. This paper discusses when this issue arises and how it can be studied with a simple example. We present a simple mass-spring system of ordinary differential equations (ODEs) to analyze accuracy and energy conservation of different coupling schemes. The ability to restore higher order of convergence by using Strang splitting or waveform iterations is verified in the context of the presented example. This paper provides details on some aspects of the talk titled 'Design and evaluation of a waveform iteration­based approach for coupling heterogeneous time stepping methods via preCICE' given at WCCM-APCOM 2022

Adaptive and flexible macro-micro coupling software

Many multiscale simulation problems require a many-to-one coupling between different scales. For such coupled problems, researchers oftentimes focus on the coupling methodology, but largely ignore software engineering and high-performance computing aspects. This can lead to inefficient use of hardware resources, on the one hand, but also inefficient use of human resources as solutions to typical technical coupling problems are constantly reinvented. This work proposes a flexible and application-agnostic software framework to couple independent simulation codes in a many-to-one fashion. To this end, we introduce a prototype of a new lightweight software component called Micro Manager, which allows us to reuse the coupling library preCICE for two-scale coupled problems. We demonstrate the applicability of the framework by a two-scale coupled heat conduction problem

CFD/CSD Coupling for an Isolated Rotor Using preCICE

Modeling a rotor blade flow field involves computing the blade motion, elastic deformation, and the three-dimensional forces and moments for specific trim conditions. Such a complex multiphysics problem, which includes a strong fluid-structure interaction, should be modeled by coupling separate solvers which are specialized on solving single-physics problems. In this work, we present a modular and extensible TAU-CAMRAD II coupling environment using the preCICE coupling library [1]. In this coupling, the aerodynamic forces and moments were computed with the CFD solver TAU. The blade control angle for the CFD simulation were determined by the CSD solver CAMRAD II. We validated the implementation using a modified model of the HART-II rotor at an advancing ratio of µ=0.3. Besides the potential that this work unlocks for future simulations of an active rotor, it also serves as an example of using preCICE for geometric multi-scale (1D-3D) coupling of closed-source solvers for periodic phenomena

Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction

We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of multi-physics simulations in general. The coupling library preCICE provides several variants, the so-called IQN-ILS method being the most commonly used. It uses input and output differences of the coupled solvers collected in previous iterations and time steps to approximate Newton iterations. To make quasi-Newton methods both applicable for parallel coupling (where these differences contain data from different physical fields) and to provide a robust approach for re-using information, a combination of information filtering and scaling for the different physical fields is typically required. This leads to good convergence, but increases the cost per iteration. We propose two new approaches—pre-scaling weight monitoring and a new, so-called QR3 filter, to substantially improve runtime while not affecting convergence quality. We evaluate these for a variety of fluid-structure interaction examples. Results show that we achieve drastic speedups for the pure quasi-Newton update steps. In the future, we intend to apply the methods also to volume-coupled scenarios, where these gains can be decisive for the feasibility of the coupling approach

Radial basis function interpolation for black-box multi-physics simulations

Interpolation based on radial basis functions (RBF) is a standard data map- ping method used in multi-physics coupling. It works on scattered data without requiring additional mesh topology or neighborhood information of support points. However, sys- tem matrices of the equations for the coefficients tend to be ill-conditioned. In this work, we illustrate the problem by a simple example and discuss possible remedies. Furthermore, we investigate the numerical performance of this method on uniform and non-uniform meshes with a particular focus on the coupling of black-box components where typically no information about the underlying discretization can be extracted. Radial basis func- tion interpolation usually uses an enhancement of the radial basis functions by a global polynomial in order to properly capture constant components and linear trends in the given data. We present a method that determines this polynomial independent from the radial basis function ansatz, which substantially improves the condition number of the remaining RBF system. Furthermore, we show that a rescaling approach can be used to either increase the accuracy or improve the condition number even further by choosing radial basis functions with a smaller support radius. The results represent an intermediate state with the aim to be integrated into the multi-physics coupling library preCICE

Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction

We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of multi-physics simulations in general. The coupling library preCICE provides several variants, the so-called IQN-ILS method being the most commonly used. It uses input and output differences of the coupled solvers collected in previous iterations and time steps to approximate Newton iterations. To make quasi-Newton methods both applicable for parallel coupling (where these differences contain data from different physical fields) and to provide a robust approach for re-using information, a combination of information filtering and scaling for the different physical fields is typically required. This leads to good convergence, but increases the cost per iteration. We propose two new approaches—pre-scaling weight monitoring and a new, so-called QR3 filter, to substantially improve runtime while not affecting convergence quality. We evaluate these for a variety of fluid-structure interaction examples. Results show that we achieve drastic speedups for the pure quasi-Newton update steps. In the future, we intend to apply the methods also to volume-coupled scenarios, where these gains can be decisive for the feasibility of the coupling approach

Efficient and Scalable Initialization of Partitioned Coupled Simulations with preCICE

preCICE is an open-source library, that provides comprehensive functionality to couple independent parallelized solver codes to establish a partitioned multi-physics multi-code simulation environment. For data communication between the respective executables at runtime, it implements a peer-to-peer concept, which renders the computational cost of the coupling per time step negligible compared to the typical run time of the coupled codes. To initialize the peer-to-peer coupling, the mesh partitions of the respective solvers need to be compared to determine the point-to-point communication channels between the processes of both codes. This initialization effort can become a limiting factor, if we either reach memory limits or if we have to re-initialize communication relations in every time step. In this contribution, we remove two remaining bottlenecks: (i) We base the neighborhood search between mesh entities of two solvers on a tree data structure to avoid quadratic complexity, and (ii) we replace the sequential gather-scatter comparison of both mesh partitions by a two-level approach that first compares bounding boxes around mesh partitions in a sequential manner, subsequently establishes pairwise communication between processes of the two solvers, and finally compares mesh partitions between connected processes in parallel. We show, that the two-level initialization method is fives times faster than the old one-level scheme on 24,567 CPU-cores using a mesh with 628,898 vertices. In addition, the two-level scheme is able to handle much larger computational meshes, since the central mesh communication of the one-level scheme is replaced with a fully point-to-point mesh communication scheme

A parallel, black-box coupling algorithm for fluid-structure interaction

The simulation of multi-physics scenarios, in particular fluid-structure interaction has gained more and more importance in the last years due to increasing accuracy requirements for a large range of applications from biomedical fields to technical design problems. At the same time, this type of simulation has become feasible due to the increased computing power of modern supercomputers. Note that only the combination of a highly accurate and, thus, highly resolved, discretization with the multi-physics model yields more detailed and more realistic results than a simple single-physics simulation. However, modern computing architectures require a good scalability of simulation methods on massively parallel systems. For fluid-structure interactions, if done in a partitioned way using separate fluid and structure codes, in particular the usually applied staggered scheme executing fluid and structure solver one after the other hinders a good scalability. This is due to the in general largely different computational costs of the two solvers. In this paper, we propose two new coupling schemes for an implicit coupling of black-box fluid and structure solvers that execute the two solvers in parallel and still yield good convergence and stability even for incompressible fluids which is shown by means of numerical results for the flow through a flexible tube