8,618 research outputs found
Discontinuous Galerkin method for the spherically reduced BSSN system with second-order operators
We present a high-order accurate discontinuous Galerkin method for evolving
the spherically-reduced Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system
expressed in terms of second-order spatial operators. Our multi-domain method
achieves global spectral accuracy and long-time stability on short
computational domains. We discuss in detail both our scheme for the BSSN system
and its implementation. After a theoretical and computational verification of
the proposed scheme, we conclude with a brief discussion of issues likely to
arise when one considers the full BSSN system.Comment: 35 pages, 6 figures, 1 table, uses revtex4. Revised in response to
referee's repor
Electrochemical Impedance Imaging via the Distribution of Diffusion Times
We develop a mathematical framework to analyze electrochemical impedance
spectra in terms of a distribution of diffusion times (DDT) for a parallel
array of random finite-length Warburg (diffusion) or Gerischer
(reaction-diffusion) circuit elements. A robust DDT inversion method is
presented based on Complex Nonlinear Least Squares (CNLS) regression with
Tikhonov regularization and illustrated for three cases of nanostructured
electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a
silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow
battery. The results demonstrate the feasibility of non-destructive "impedance
imaging" to infer microstructural statistics of random, heterogeneous
materials
PDEs with Compressed Solutions
Sparsity plays a central role in recent developments in signal processing,
linear algebra, statistics, optimization, and other fields. In these
developments, sparsity is promoted through the addition of an norm (or
related quantity) as a constraint or penalty in a variational principle. We
apply this approach to partial differential equations that come from a
variational quantity, either by minimization (to obtain an elliptic PDE) or by
gradient flow (to obtain a parabolic PDE). Also, we show that some PDEs can be
rewritten in an form, such as the divisible sandpile problem and
signum-Gordon. Addition of an term in the variational principle leads to
a modified PDE where a subgradient term appears. It is known that modified PDEs
of this form will often have solutions with compact support, which corresponds
to the discrete solution being sparse. We show that this is advantageous
numerically through the use of efficient algorithms for solving based
problems.Comment: 21 pages, 15 figure
A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations
In this paper, we develop regularized discrete least squares collocation and
finite volume methods for solving two-dimensional nonlinear time-dependent
partial differential equations on irregular domains. The solution is
approximated using tensor product cubic spline basis functions defined on a
background rectangular (interpolation) mesh, which leads to high spatial
accuracy and straightforward implementation, and establishes a solid base for
extending the computational framework to three-dimensional problems. A
semi-implicit time-stepping method is employed to transform the nonlinear
partial differential equation into a linear boundary value problem. A key
finding of our study is that the newly proposed mesh-free finite volume method
based on circular control volumes reduces to the collocation method as the
radius limits to zero. Both methods produce a large constrained least-squares
problem that must be solved at each time step in the advancement of the
solution. We have found that regularization yields a relatively
well-conditioned system that can be solved accurately using QR factorization.
An extensive numerical investigation is performed to illustrate the
effectiveness of the present methods, including the application of the new
method to a coupled system of time-fractional partial differential equations
having different fractional indices in different (irregularly shaped) regions
of the solution domain
Semidirect computation of three-dimensional viscous flows over suction holes in laminar flow control surfaces
A summary is given of the attempts made to apply semidirect methods to the calculation of three-dimensional viscous flows over suction holes in laminar flow control surfaces. The attempts were all unsuccessful, due to either (1) lack of resolution capability, (2) lack of computer efficiency, or (3) instability
The MOLDY short-range molecular dynamics package
We describe a parallelised version of the MOLDY molecular dynamics program.
This Fortran code is aimed at systems which may be described by short-range
potentials and specifically those which may be addressed with the embedded atom
method. This includes a wide range of transition metals and alloys. MOLDY
provides a range of options in terms of the molecular dynamics ensemble used
and the boundary conditions which may be applied. A number of standard
potentials are provided, and the modular structure of the code allows new
potentials to be added easily. The code is parallelised using OpenMP and can
therefore be run on shared memory systems, including modern multicore
processors. Particular attention is paid to the updates required in the main
force loop, where synchronisation is often required in OpenMP implementations
of molecular dynamics. We examine the performance of the parallel code in
detail and give some examples of applications to realistic problems, including
the dynamic compression of copper and carbon migration in an iron-carbon alloy
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