GPU‐based Polynomial Finite Element Matrix Assembly for Simplex Meshes

Mueller-Roemer, Johannes Sebastian; Sourander, André

doi:10.1111/cgf.13581

Cited by 11 publications

(6 citation statements)

References 30 publications

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“…In the case of direct solvers, the assembly of the global matrix is required to compute the decomposition or factorisation of the system. Dziekonski et al 25 and Mueller et al 26 proposed to assemble the matrix directly on the GPU thus reducing memory transfer and speeding up the assembly. In this case also, the method requires a model specific algorithm and cannot provide a good combination of heterogeneous CPU/GPU simulations.…”

Section: Gpu-accelerationmentioning

confidence: 99%

DeepPhysics: a physics aware deep learning framework for real-time simulation

Odot,

Haferssas,

Cotin

2021

Preprint

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Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of reference for solving the partial differential equations associated with these problems. Yet, deep learning methods have recently shown that they could represent an alternative strategy to solve physics-based problems 1,2,3 . In this paper, we propose a solution to simulate hyper-elastic materials using a data-driven approach, where a neural network is trained to learn the non-linear relationship between boundary conditions and the resulting displacement field. We also introduce a method to guarantee the validity of the solution. In total, we present three contributions: an optimized data set generation algorithm based on modal analysis, a physics-informed loss function, and a Hybrid Newton-Raphson algorithm. The method is applied to two benchmarks: a cantilever beam and a propeller. The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond. The predictions on various geometries, topologies, mesh resolutions, and boundary conditions are accurate to a few micrometers for non-linear deformations of several centimeters of amplitude.

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Section: Gpu-accelerationmentioning

confidence: 99%

DeepPhysics: a physics aware deep learning framework for real-time simulation

Odot,

Haferssas,

Cotin

2021

Preprint

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“…Workload is generated via the finite element (FE) simulation RISTRA [17]. RISTRA is a highly optimized, GPUaccelerated FE simulation package that performs both system assembly [18] and solution [19] on the GPU, while making use of the 3×3-block structure of the system matrices [20].…”

Section: A Iot Devicementioning

confidence: 99%

Generative Machine Learning for Resource-Aware 5G and IoT Systems

Piatkowski

Mueller-Roemer

Hasse

et al. 2021

2021 IEEE International Conference on Communications Workshops (ICC Workshops)

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Extrapolations predict that the sheer number of Internet-of-Things (IoT) devices will exceed 40 billion in the next five years. Hand-crafting specialized energy models and monitoring sub-systems for each type of device is error prone, costly, and sometimes infeasible. In order to detect abnormal or faulty behavior as well as inefficient resource usage autonomously, it is of tremendous importance to endow upcoming IoT and 5G devices with sufficient intelligence to deduce an energy model from their own resource usage data. Such models can in-turn be applied to predict upcoming resource consumption and to detect system behavior that deviates from normal states. To this end, we investigate a special class of undirected probabilistic graphical model, the so-called integer Markov random fields (IntMRF). On the one hand, this model learns a full generative probability distribution over all possible states of the system-allowing us to predict system states and to measure the probability of observed states. On the other hand, IntMRFs are themselves designed to consume as less resources as possible-e.g., faithful modelling of systems with an exponentially large number of states, by using only 8-bit unsigned integer arithmetic and less than 16KB memory. We explain how IntMRFs can be applied to model the resource consumption and the system behavior of an IoT device and a 5G core network component, both under various workloads. Our results suggest, that the machine learning model can represent important characteristics of our two test systems and deliver reasonable predictions of the power consumption.

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“…To achieve direct, low-latency simulation feedback, we use a fully GPU-accelerated FEA code based on the merged kernel modified preconditioned conjugate gradient (MPCG) solver by We-ber el al. (Weber et al, 2013) and the fast tetrahedral system assembly method by Mueller-Roemer and Stork (Mueller-Roemer and Stork, 2018). As Mueller-Roemer and Stork's method not only performs element stiffness matrix assembly on the GPU, but also determines the system matrix sparsity pattern efficiently in parallel, it is highly beneficial when not only tetrahedral mesh geometry, but also topology, is modified during editing.…”

Section: Related Workmentioning

confidence: 99%

TEdit: A Distributed Tetrahedral Mesh Editor with Immediate Simulation Feedback

Ströter

Krispel

Mueller-Roemer

et al. 2021

Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

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The cycle of computer aided design and verification via physics simulation is often burdened by the use of separate tools for modeling and simulation, which requires conversion between formats, e.g. meshing for finite element simulation. This separation is often unavoidable because the tools contain specific domain knowledge which is mandatory for the task, for example a specific CAD modeling suite. We propose a distributed application that allows interactive modification of tetrahedral meshes, derived from existing CAD models. It provides immediate simulation feedback by offloading resource-intensive tasks onto multiple machines thereby enabling fast design cycles for individualized versions of mass-produced parts.

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GPU‐based Polynomial Finite Element Matrix Assembly for Simplex Meshes

Cited by 11 publications

References 30 publications

DeepPhysics: a physics aware deep learning framework for real-time simulation

DeepPhysics: a physics aware deep learning framework for real-time simulation

Generative Machine Learning for Resource-Aware 5G and IoT Systems

TEdit: A Distributed Tetrahedral Mesh Editor with Immediate Simulation Feedback

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