55,421 research outputs found
Fast cubature of volume potentials over rectangular domains
In the present paper we study high-order cubature formulas for the
computation of advection-diffusion potentials over boxes. By using the basis
functions introduced in the theory of approximate approximations, the cubature
of a potential is reduced to the quadrature of one dimensional integrals. For
densities with separated approximation, we derive a tensor product
representation of the integral operator which admits efficient cubature
procedures in very high dimensions. Numerical tests show that these formulas
are accurate and provide approximation of order up to dimension
.Comment: 17 page
Pruning Algorithms for Pretropisms of Newton Polytopes
Pretropisms are candidates for the leading exponents of Puiseux series that
represent solutions of polynomial systems. To find pretropisms, we propose an
exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton
polytopes. We prefer exact arithmetic not only because of the exact input and
the degrees of the output, but because of the often unpredictable growth of the
coordinates in the face normals, even for polytopes in generic position. We
provide experimental results with our preliminary implementation in Sage that
compare favorably with the pruning method that relies only on cone
intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning,
accepted for presentation at Computer Algebra in Scientific Computing, CASC
201
A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
In this paper we formulate and test numerically a fully-coupled discontinuous
Galerkin (DG) method for incompressible two-phase flow with discontinuous
capillary pressure. The spatial discretization uses the symmetric interior
penalty DG formulation with weighted averages and is based on a wetting-phase
potential / capillary potential formulation of the two-phase flow system. After
discretizing in time with diagonally implicit Runge-Kutta schemes the resulting
systems of nonlinear algebraic equations are solved with Newton's method and
the arising systems of linear equations are solved efficiently and in parallel
with an algebraic multigrid method. The new scheme is investigated for various
test problems from the literature and is also compared to a cell-centered
finite volume scheme in terms of accuracy and time to solution. We find that
the method is accurate, robust and efficient. In particular no post-processing
of the DG velocity field is necessary in contrast to results reported by
several authors for decoupled schemes. Moreover, the solver scales well in
parallel and three-dimensional problems with up to nearly 100 million degrees
of freedom per time step have been computed on 1000 processors
Kernel Ellipsoidal Trimming
Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered information matrix. Although the method is very general and can be applied to many of the aforementioned problems, the main focus in this paper is the problem of novelty or outlier detection associated with fault detection. A simple iterative algorithm based on Titterington's minimum volume ellipsoid method is proposed for practical implementation. The KIMEE method demonstrates very good performance on a set of real-life and simulated datasets compared with support vector machine methods
Proper orthogonal decomposition closure models for fluid flows: Burgers equation
This paper puts forth several closure models for the proper orthogonal
decomposition (POD) reduced order modeling of fluid flows. These new closure
models, together with other standard closure models, are investigated in the
numerical simulation of the Burgers equation. This simplified setting
represents just the first step in the investigation of the new closure models.
It allows a thorough assessment of the performance of the new models, including
a parameter sensitivity study. Two challenging test problems displaying moving
shock waves are chosen in the numerical investigation. The closure models and a
standard Galerkin POD reduced order model are benchmarked against the fine
resolution numerical simulation. Both numerical accuracy and computational
efficiency are used to assess the performance of the models
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