66 research outputs found
Problems in computational helioseismology
We discuss current advances in forward and inverse modeling for local
helioseismology. We report theoretical uniqueness results, in particular the
Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the
non-linear inverse problem of time-distance helioseismology (finite amplitude
pertubations to the medium). Numerical experiments were conducted to determine
the number of frequencies required to reconstruct density and sound speed in
the solar interior.Comment: Oberwolfach Report, Computational Inverse Problems for Partial
Differential Equations, 14 May - 20 May 2017.
https://www.mfo.de/occasion/1720/www_vie
Overview on a selection of recent works in asymptotic analysis for wave propagation problems
We give a brief survey of some recent advances of asymptotic analysis methods applied to wave propagation problem
Low-order continuous finite element spaces on hybrid non-conforming hexahedral-tetrahedral meshes
This article deals with solving partial differential equations with the
finite element method on hybrid non-conforming hexahedral-tetrahedral meshes.
By non-conforming, we mean that a quadrangular face of a hexahedron can be
connected to two triangular faces of tetrahedra. We introduce a set of
low-order continuous (C0) finite element spaces defined on these meshes. They
are built from standard tri-linear and quadratic Lagrange finite elements with
an extra set of constraints at non-conforming hexahedra-tetrahedra junctions to
recover continuity. We consider both the continuity of the geometry and the
continuity of the function basis as follows: the continuity of the geometry is
achieved by using quadratic mappings for tetrahedra connected to tri-affine
hexahedra and the continuity of interpolating functions is enforced in a
similar manner by using quadratic Lagrange basis on tetrahedra with constraints
at non-conforming junctions to match tri-linear hexahedra. The so-defined
function spaces are validated numerically on simple Poisson and linear
elasticity problems for which an analytical solution is known. We observe that
using a hybrid mesh with the proposed function spaces results in an accuracy
significantly better than when using linear tetrahedra and slightly worse than
when solely using tri-linear hexahedra. As a consequence, the proposed function
spaces may be a promising alternative for complex geometries that are out of
reach of existing full hexahedral meshing methods
C2 representations of the solar background coefficients for the model S-AtmoI
We construct C2 representations of the background quantities that
characterize the interior of the Sun and its atmosphere starting from the
data-points of the standard solar model S. This model is further extended
considering an isothermal atmosphere, that we refer to as model AtmoI. It is
not trivial to build the C2 representations of the parameters from a discrete
set of values, in particular in the transition region between the end of model
S and the atmosphere. This technical work is needed as a crucial building block
to study theoretically and numerically the propagation of waves in the Sun,
using the equations of solar oscillations (also referred to as Galbrun's
equation in aeroacoustics). The constructed models are available at
http://phaidra.univie.ac.at/o:1097638.Comment: 17 page
Time-decoupled high order continuous space-time finite element schemes for the heat equation
Copyright © by SIAMIn Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6685—6708 Werder et al. demonstrated that time discretizations of the heat equation by a temporally discontinuous Galerkin finite element method could be decoupled by diagonalising the temporal ‘Gram matrices’. In this article we propose a companion approach for the heat equation by using a continuous Galerkin time discretization. As a result, if piecewise polynomials of degree d are used as the trial functions in time and the spatial discretization produces systems of dimension M then, after decoupling, d systems of size M need to be solved rather than a single system of sizeMd. These decoupled systems require complex arithmetic, as did Werder et al.’s technique, but are amenable to parallel solution on modern multi-core architectures. We give numerical tests for temporal polynomial degrees up to six for three different model test problems, using both Galerkin and spectral element spatial discretizations, and show convergence and temporal superconvergence rates that accord with the bounds given by Aziz and Monk, Math. Comp. 52:186 (1989), pp. 255—274. We also interpret error as a function of computational time and see that our high order schemes may offer greater efficiency that the Crank-Nicolson method in terms of accuracy per unit of computational time—although in a multi-core world, with highly tuned iterative solvers, one has to be cautious with such claims. We close with a speculation on the application of these ideas to the Navier-Stokes equations for incompressible fluids
Fall Concert of the Chapman University Choir, University Singers, and University Women\u27s Chorus
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