FMMTL: FMM Template Library A Generalized Framework for Kernel Matrices

Cecka, Cris; Layton, Simon K.

doi:10.1007/978-3-319-10705-9_60

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…The linking integrand uses the Green's function for the Laplace problem in a Biot-Savart integral, and there are numerous Fast Multipole libraries for the Laplace problem, including FMM3D [Cheng et al 1999] and FMMTL [Cecka and Layton 2015]. FMMTL provides an implementation of the Biot-Savart integral and has recently been used to simulate ferrofluids in graphics [Huang et al 2019].…”

Section: Related Workmentioning

confidence: 99%

Fast linking numbers for topology verification of loopy structures

James

2021

ACM Trans. Graph.

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It is increasingly common to model, simulate, and process complex materials based on loopy structures, such as in yarn-level cloth garments, which possess topological constraints between inter-looping curves. While the input model may satisfy specific topological linkages between pairs of closed loops, subsequent processing may violate those topological conditions. In this paper, we explore a family of methods for efficiently computing and verifying linking numbers between closed curves, and apply these to applications in geometry processing, animation, and simulation, so as to verify that topological invariants are preserved during and after processing of the input models. Our method has three stages: (1) we identify potentially interacting loop-loop pairs, then (2) carefully discretize each loop's spline curves into line segments so as to enable (3) efficient linking number evaluation using accelerated kernels based on either counting projected segment-segment crossings, or by evaluating the Gauss linking integral using direct or fast summation methods (Barnes-Hut or fast multipole methods). We evaluate CPU and GPU implementations of these methods on a suite of test problems, including yarn-level cloth and chainmail, that involve significant processing: physics-based relaxation and animation, user-modeled deformations, curve compression and reparameterization. We show that topology errors can be efficiently identified to enable more robust processing of loopy structures.

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Section: Related Workmentioning

confidence: 99%

Fast linking numbers for topology verification of loopy structures

James

2021

ACM Trans. Graph.

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“…FMMTL (Cecka & Layton, 2015) is another existing FMM library with a generic C++ design. Similar to TBFMM, FMMTL works with various types of kernels.…”

Section: Statement Of Needmentioning

confidence: 99%

TBFMM: A C++ generic and parallel fast multipole method library

Bramas¹

2020

JOSS

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TBFMM, for task-based FMM, is a high-performance package that implements the parallel fast multipole method (FMM) in modern C++17. It implements parallel strategies for multicore architectures, i.e. to run on a single computing node. TBFMM was designed to be easily customized thanks to C++ templates and fine control of the C++ classes' inter-dependencies. Users can implement new FMM kernels, new types of interacting elements or even new parallelization strategies. As such, it can be used as a simulation toolbox for scientists in physics or applied mathematics. It enables users to perform simulations while delegating the data structure, the algorithm and the parallelization to the library. Besides, TBFMM can also provide an interesting use case for the HPC research community regarding parallelization, optimization and scheduling of applications handling irregular data structures.

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“…During the solving process, the particles' positions are fixed, so the tree structures of the FMM does not need to be reconstructed in every iteration, saving the expensive overhead. We use the FMMTL library [Cecka and Layton 2015] to calculate the summation. The performance comparison is illustrated in Figure 7.…”

Section: Magnetizationmentioning

confidence: 99%

“…Within the FMMTL library [Cecka and Layton 2015], the solver for the electric potential of a cluster of point charges is already implemented. It is is based on the same equation as magnetic and gravitational potentials.…”

Section: Magnetizationmentioning

confidence: 99%

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On the accurate large-scale simulation of ferrofluids

2019

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Fig. 1. Our approach can accurately reproduce the observation that real ferrofluid is literally climbing up a steel helix placed above a strong electromagnet. This figure shows the final results of our simulation of this scenario rendered from different viewpoints. We present an approach to the accurate and efficient large-scale simulation of the complex dynamics of ferrofluids based on physical principles. Ferrofluids are liquids containing magnetic particles that react to an external magnetic field without solidifying. In this contribution, we employ smooth magnets to simulate ferrofluids in contrast to previous methods based on the finite element method or point magnets. We solve the magnetization using the analytical solution of the smooth magnets' field, and derive the bounded magnetic force formulas addressing particle penetration. We integrate the magnetic field and force evaluations into the fast multipole method allowing for efficient large-scale simulations of ferrofluids. The presented simulations are well reproducible since our approach can be easily incorporated into a framework implementing a Fast Multipole Method and a Smoothed Particle Hydrodynamics fluid solver with surface tension. We provide a detailed analysis of our approach and validate our results against real wet lab experiments. This work can potentially open the door for a deeper understanding of ferrofluids and for the identification of new areas of applications of these materials.

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FMMTL: FMM Template Library A Generalized Framework for Kernel Matrices

Cited by 5 publications

References 13 publications

Fast linking numbers for topology verification of loopy structures

Fast linking numbers for topology verification of loopy structures

TBFMM: A C++ generic and parallel fast multipole method library

On the accurate large-scale simulation of ferrofluids

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