4,036 research outputs found
Evaluating kernels on Xeon Phi to accelerate Gysela application
This work describes the challenges presented by porting parts ofthe Gysela
code to the Intel Xeon Phi coprocessor, as well as techniques used for
optimization, vectorization and tuning that can be applied to other
applications. We evaluate the performance of somegeneric micro-benchmark on Phi
versus Intel Sandy Bridge. Several interpolation kernels useful for the Gysela
application are analyzed and the performance are shown. Some memory-bound and
compute-bound kernels are accelerated by a factor 2 on the Phi device compared
to Sandy architecture. Nevertheless, it is hard, if not impossible, to reach a
large fraction of the peek performance on the Phi device,especially for
real-life applications as Gysela. A collateral benefit of this optimization and
tuning work is that the execution time of Gysela (using 4D advections) has
decreased on a standard architecture such as Intel Sandy Bridge.Comment: submitted to ESAIM proceedings for CEMRACS 2014 summer school version
reviewe
A family of quadrilateral finite elements
We present a novel family of quadrilateral finite elements, which
define global spaces over a general quadrilateral mesh with vertices of
arbitrary valency. The elements extend the construction by (Brenner and Sung,
J. Sci. Comput., 2005), which is based on polynomial elements of tensor-product
degree , to all degrees . Thus, we call the family of
finite elements Brenner-Sung quadrilaterals. The proposed quadrilateral
can be seen as a special case of the Argyris isogeometric element of (Kapl,
Sangalli and Takacs, CAGD, 2019). The quadrilateral elements possess similar
degrees of freedom as the classical Argyris triangles. Just as for the Argyris
triangle, we additionally impose continuity at the vertices. In this
paper we focus on the lower degree cases, that may be desirable for their lower
computational cost and better conditioning of the basis: We consider indeed the
polynomial quadrilateral of (bi-)degree~, and the polynomial degrees
and by employing a splitting into or polynomial
pieces, respectively.
The proposed elements reproduce polynomials of total degree . We show that
the space provides optimal approximation order. Due to the interpolation
properties, the error bounds are local on each element. In addition, we
describe the construction of a simple, local basis and give for
explicit formulas for the B\'{e}zier or B-spline coefficients of the basis
functions. Numerical experiments by solving the biharmonic equation demonstrate
the potential of the proposed quadrilateral finite element for the
numerical analysis of fourth order problems, also indicating that (for )
the proposed element performs comparable or in general even better than the
Argyris triangle with respect to the number of degrees of freedom
Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
We present a new approach to three-dimensional electromagnetic scattering
problems via fast isogeometric boundary element methods. Starting with an
investigation of the theoretical setting around the electric field integral
equation within the isogeometric framework, we show existence, uniqueness, and
quasi-optimality of the isogeometric approach. For a fast and efficient
computation, we then introduce and analyze an interpolation-based fast
multipole method tailored to the isogeometric setting, which admits competitive
algorithmic and complexity properties. This is followed by a series of
numerical examples of industrial scope, together with a detailed presentation
and interpretation of the results
Information-Theoretic Registration with Explicit Reorientation of Diffusion-Weighted Images
We present an information-theoretic approach to the registration of images
with directional information, and especially for diffusion-Weighted Images
(DWI), with explicit optimization over the directional scale. We call it
Locally Orderless Registration with Directions (LORD). We focus on normalized
mutual information as a robust information-theoretic similarity measure for
DWI. The framework is an extension of the LOR-DWI density-based hierarchical
scale-space model that varies and optimizes the integration, spatial,
directional, and intensity scales. As affine transformations are insufficient
for inter-subject registration, we extend the model to non-rigid deformations.
We illustrate that the proposed model deforms orientation distribution
functions (ODFs) correctly and is capable of handling the classic complex
challenges in DWI-registrations, such as the registration of fiber-crossings
along with kissing, fanning, and interleaving fibers. Our experimental results
clearly illustrate a novel promising regularizing effect, that comes from the
nonlinear orientation-based cost function. We show the properties of the
different image scales and, we show that including orientational information in
our model makes the model better at retrieving deformations in contrast to
standard scalar-based registration.Comment: 16 pages, 19 figure
Solving the Monge-Amp\`ere Equations for the Inverse Reflector Problem
The inverse reflector problem arises in geometrical nonimaging optics: Given
a light source and a target, the question is how to design a reflecting
free-form surface such that a desired light density distribution is generated
on the target, e.g., a projected image on a screen. This optical problem can
mathematically be understood as a problem of optimal transport and equivalently
be expressed by a secondary boundary value problem of the Monge-Amp\`ere
equation, which consists of a highly nonlinear partial differential equation of
second order and constraints. In our approach the Monge-Amp\`ere equation is
numerically solved using a collocation method based on tensor-product
B-splines, in which nested iteration techniques are applied to ensure the
convergence of the nonlinear solver and to speed up the calculation. In the
numerical method special care has to be taken for the constraint: It enters the
discrete problem formulation via a Picard-type iteration. Numerical results are
presented as well for benchmark problems for the standard Monge-Amp\`ere
equation as for the inverse reflector problem for various images. The designed
reflector surfaces are validated by a forward simulation using ray tracing.Comment: 28 pages, 8 figures, 2 tables; Keywords: Inverse reflector problem,
elliptic Monge-Amp\`ere equation, B-spline collocation method, Picard-type
iteration; Minor revision: reference [59] to a recent preprint has been added
and a few typos have been correcte
Particle tracking methods for residence time calculations in incompressible flow
Numerical methods are presented for the calculation of residence time distributions in steady incompressible fluid flow using a given set of normal fluid fluxes, defined across the cell faces of a cartesian tensor product mesh. A particle tracking approach is adopted involving the construction of a piecewise polynomial representation of the velocity distribution, and subsequent integration of this representation for the determination of individual particle trajectories
Doctor of Philosophy
dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest
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