Kernel-independent fast multipole method within the framework of regularized Stokeslets

Rostami, Minghao W.; Olson, Sarah D.

doi:10.1016/j.jfluidstructs.2016.07.006

Cited by 24 publications

(60 citation statements)

References 52 publications

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“…To handle the removable singularity, we adopt the procedure in [3] (page 510), see also [27]; the code checks whether a source particle coordinate is close to a Chebyshev point; the condition is |y jl − s k | ≤ DBL_MIN, where DBL_MIN = 2.22507e-308 is the smallest positive IEEE double precision oating point number; if this condition is met, then the temporary variables c j,k, , d j,k, are adjusted to enforce the interpolation conditions (8). Having computed the temporary variables c j,k, , d j,k, , the code computes the Hermite basis functions in (20), and then the modi ed charges are computed as indicated in (19). For each cluster this process requires O(n Nc) operations and O(n ) storage.…”

Section: Computation Of Modi Ed Chargesmentioning

confidence: 99%

“…Although we demonstrated the method for electrostatic potentials, it can be extended to compute electrostatic forces arising from Coulomb and screened Coulomb potentials, as needed in molecular dynamics simulations. It would also be interesting to consider whether the BHTC is advantageous for more complicated kernels such as those arising in the Method of Regularized Stokeslets [5,6,20]. We plan to install the BHTC in the Table 3: Barycentric Hermite treecode parallel performance, random particles in a cube, system size N=1e6, treecode parameters MAC θ = .…”

Section: Parallel Simulationsmentioning

confidence: 99%

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A treecode based on barycentric Hermite interpolation for electrostatic particle interactions

Krasny

Wang

2019

Computational and Mathematical Biophysics

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A particle-cluster treecode based on barycentric Hermite interpolation is presented for fast summation of electrostatic particle interactions in 3D. The interpolation nodes are Chebyshev points of the 2nd kind in each cluster. It is noted that barycentric Hermite interpolation is scale-invariant in a certain sense that promotes the treecode’s efficiency. Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system. The advantage of the barycentric Hermite treecode is demonstrated in comparison with treecodes based on Taylor approximation and barycentric Lagrange interpolation.

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Section: Computation Of Modi Ed Chargesmentioning

confidence: 99%

Section: Parallel Simulationsmentioning

confidence: 99%

A treecode based on barycentric Hermite interpolation for electrostatic particle interactions

Krasny

Wang

2019

Computational and Mathematical Biophysics

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“…The near-field data is solved with the direct method, while the far-field data is solved with the approximate method within a certain error range. Therefore, the speed of interpolation calculations can greatly be improved [29,30].…”

Section: Fast Reconstructionmentioning

confidence: 99%

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

et al. 2019

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In this paper, we present an improved approach to the surface reconstruction of orebody from sets of interpreted cross sections that allows for shape control with geometry constraints. The soft and hard constraint rules based on adaptive sampling are proposed. As only the internal and external position relations of sections are calculated, it is unnecessary to estimate the normal directions of sections. Our key contribution is proposing an iterative closest point correction algorithm. It can be used for iterative correction of the distance field based on the constraint rules and the internal and external position relations of the model. We develop a rich variety of geometry constraints to dynamically control the shape trend of orebody for structural geologists. As both of the processes of interpolation and iso-surface extraction are improved, the performance of this method is excellent. Combined with the interactive tools of constraint rules, our approach is shown to be effective on non-trivial sparse sections. We show the reconstruction results with real geological datasets and compare the method with the existing reconstruction methods.

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“…Substituting equation (20) and equation (21) into equation (19), we have S[ , n] = − 2n + 3 2(n + 1)…”

Section: By Taylor's Theorem We Havementioning

confidence: 99%

A New Family of Regularized Kernels for the Harmonic Oscillator

2016

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In this paper, a new two-parameter family of regularized kernels is introduced, suitable for applying high-order time stepping to N-body systems. These high-order kernels are derived by truncating a Taylor expansion of the nonregularized kernel about (r 2 + 2 ), generating a sequence of increasingly more accurate kernels. This paper proves the validity of this two-parameter family of regularized kernels, constructs error estimates, and illustrates the benefits of using high-order kernels through numerical experiments.

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Kernel-independent fast multipole method within the framework of regularized Stokeslets

Cited by 24 publications

References 52 publications

A treecode based on barycentric Hermite interpolation for electrostatic particle interactions

A treecode based on barycentric Hermite interpolation for electrostatic particle interactions

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

A New Family of Regularized Kernels for the Harmonic Oscillator

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