18,178 research outputs found
Piecewise smooth chebfuns
Algorithms are described that make it possible to manipulate piecewise-smooth functions on real intervals numerically with close to machine precision. Breakpoints are introduced in some such calculations at points determined by numerical rootfinding, and in others by recursive subdivision or automatic edge detection. Functions are represented on each smooth subinterval by Chebyshev series or interpolants. The algorithms are implemented in object-oriented MATLAB in an extension of the chebfun system, which was previously limited to smooth functions on [-1, 1]
Parallel eigensolvers in plane-wave Density Functional Theory
We consider the problem of parallelizing electronic structure computations in
plane-wave Density Functional Theory. Because of the limited scalability of
Fourier transforms, parallelism has to be found at the eigensolver level. We
show how a recently proposed algorithm based on Chebyshev polynomials can scale
into the tens of thousands of processors, outperforming block conjugate
gradient algorithms for large computations
Memristors for the Curious Outsiders
We present both an overview and a perspective of recent experimental advances
and proposed new approaches to performing computation using memristors. A
memristor is a 2-terminal passive component with a dynamic resistance depending
on an internal parameter. We provide an brief historical introduction, as well
as an overview over the physical mechanism that lead to memristive behavior.
This review is meant to guide nonpractitioners in the field of memristive
circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page
Hyperelliptic Theta-Functions and Spectral Methods
A code for the numerical evaluation of hyperelliptic theta-functions is
presented. Characteristic quantities of the underlying Riemann surface such as
its periods are determined with the help of spectral methods. The code is
optimized for solutions of the Ernst equation where the branch points of the
Riemann surface are parameterized by the physical coordinates. An exploration
of the whole parameter space of the solution is thus only possible with an
efficient code. The use of spectral approximations allows for an efficient
calculation of all quantities in the solution with high precision. The case of
almost degenerate Riemann surfaces is addressed. Tests of the numerics using
identities for periods on the Riemann surface and integral identities for the
Ernst potential and its derivatives are performed. It is shown that an accuracy
of the order of machine precision can be achieved. These accurate solutions are
used to provide boundary conditions for a code which solves the axisymmetric
stationary Einstein equations. The resulting solution agrees with the
theta-functional solution to very high precision.Comment: 25 pages, 12 figure
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