8,526 research outputs found
Fast Ewald summation for free-space Stokes potentials
We present a spectrally accurate method for the rapid evaluation of
free-space Stokes potentials, i.e. sums involving a large number of free space
Green's functions. We consider sums involving stokeslets, stresslets and
rotlets that appear in boundary integral methods and potential methods for
solving Stokes equations. The method combines the framework of the Spectral
Ewald method for periodic problems, with a very recent approach to solving the
free-space harmonic and biharmonic equations using fast Fourier transforms
(FFTs) on a uniform grid. Convolution with a truncated Gaussian function is
used to place point sources on a grid. With precomputation of a scalar grid
quantity that does not depend on these sources, the amount of oversampling of
the grids with Gaussians can be kept at a factor of two, the minimum for
aperiodic convolutions by FFTs. The resulting algorithm has a computational
complexity of O(N log N) for problems with N sources and targets. Comparison is
made with a fast multipole method (FMM) to show that the performance of the new
method is competitive.Comment: 35 pages, 15 figure
High-order Discretization of a Gyrokinetic Vlasov Model in Edge Plasma Geometry
We present a high-order spatial discretization of a continuum gyrokinetic
Vlasov model in axisymmetric tokamak edge plasma geometries. Such models
describe the phase space advection of plasma species distribution functions in
the absence of collisions. The gyrokinetic model is posed in a four-dimensional
phase space, upon which a grid is imposed when discretized. To mitigate the
computational cost associated with high-dimensional grids, we employ a
high-order discretization to reduce the grid size needed to achieve a given
level of accuracy relative to lower-order methods. Strong anisotropy induced by
the magnetic field motivates the use of mapped coordinate grids aligned with
magnetic flux surfaces. The natural partitioning of the edge geometry by the
separatrix between the closed and open field line regions leads to the
consideration of multiple mapped blocks, in what is known as a mapped
multiblock (MMB) approach. We describe the specialization of a more general
formalism that we have developed for the construction of high-order,
finite-volume discretizations on MMB grids, yielding the accurate evaluation of
the gyrokinetic Vlasov operator, the metric factors resulting from the MMB
coordinate mappings, and the interaction of blocks at adjacent boundaries. Our
conservative formulation of the gyrokinetic Vlasov model incorporates the fact
that the phase space velocity has zero divergence, which must be preserved
discretely to avoid truncation error accumulation. We describe an approach for
the discrete evaluation of the gyrokinetic phase space velocity that preserves
the divergence-free property to machine precision
An Algorithmic Framework for Efficient Large-Scale Circuit Simulation Using Exponential Integrators
We propose an efficient algorithmic framework for time domain circuit
simulation using exponential integrator. This work addresses several critical
issues exposed by previous matrix exponential based circuit simulation
research, and makes it capable of simulating stiff nonlinear circuit system at
a large scale. In this framework, the system's nonlinearity is treated with
exponential Rosenbrock-Euler formulation. The matrix exponential and vector
product is computed using invert Krylov subspace method. Our proposed method
has several distinguished advantages over conventional formulations (e.g., the
well-known backward Euler with Newton-Raphson method). The matrix factorization
is performed only for the conductance/resistance matrix G, without being
performed for the combinations of the capacitance/inductance matrix C and
matrix G, which are used in traditional implicit formulations. Furthermore, due
to the explicit nature of our formulation, we do not need to repeat LU
decompositions when adjusting the length of time steps for error controls. Our
algorithm is better suited to solving tightly coupled post-layout circuits in
the pursuit for full-chip simulation. Our experimental results validate the
advantages of our framework.Comment: 6 pages; ACM/IEEE DAC 201
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Comparison of Current Gravity Estimation and Determination Models
This paper will discuss the history of gravity estimation and determination models while analyzing methods that are in development. Some fundamental methods for calculating the gravity field include spherical harmonics solutions, local weighted interpolation, and global point mascon modeling (PMC). Recently, high accuracy measurements have become more accessible, and the requirements for high order geopotential modeling have become more stringent. Interest in irregular bodies, accurate models of the hydrological system, and on-board processing has demanded a comprehensive model that can quickly and accurately compute the geopotential with low memory costs. This trade study of current geopotential modeling techniques will reveal that each modeling technique has a unique use case. It is notable that the spherical harmonics model is relatively accurate but poses a cumbersome inversion problem. PMC and interpolation models, on the other hand, are computationally efficient, but require more research to become robust models with high levels of accuracy. Considerations of the trade study will suggest further research for the point mascon model. The PMC model should be improved through mascon refinement, direct solutions that stem from geodetic measurements, and further validation of the gravity gradient. Finally, the potential for each model to be implemented with parallel computation will be shown to lead to large improvements in computing time while reducing the memory cost for each technique.Aerospace Engineering and Engineering Mechanic
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