1,749 research outputs found
Optimization of transistor design including large signal device/circuit interactions at extremely high frequencies (20-100+GHz)
Transistor design for extremely high frequency applications requires consideration of the interaction between the device and the circuit to which it is connected. Traditional analytical transistor models are to approximate at some of these frequencies and may not account for variations of dopants and semiconductor materials (especially some of the newer materials) within the device. Physically based models of device performance are required. These are based on coupled systems of partial differential equations and typically require 20 minutes of Cray computer time for a single AC operating point. A technique is presented to extract parameters from a few partial differential equation solutions for the device to create a nonlinear equivalent circuit model which runs in approximately 1 second of personal computer time. This nonlinear equivalent circuit model accurately replicates the contact current properties of the device as computed by the partial differential solver on which it is based. Using the nonlinear equivalent circuit model of the device, optimization of systems design can be performed based on device/circuit interactions
Anisotropic Fast-Marching on cartesian grids using Lattice Basis Reduction
We introduce a modification of the Fast Marching Algorithm, which solves the
generalized eikonal equation associated to an arbitrary continuous riemannian
metric, on a two or three dimensional domain. The algorithm has a logarithmic
complexity in the maximum anisotropy ratio of the riemannian metric, which
allows to handle extreme anisotropies for a reduced numerical cost. We prove
the consistence of the algorithm, and illustrate its efficiency by numerical
experiments. The algorithm relies on the computation at each grid point of a
special system of coordinates: a reduced basis of the cartesian grid, with
respect to the symmetric positive definite matrix encoding the desired
anisotropy at this point.Comment: 28 pages, 12 figure
Black box probabilistic numerics
Peer reviewe
An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems
This article presents a new approach to the real-time solution of inverse
problems on embedded systems. The class of problems addressed corresponds to
ordinary differential equations (ODEs) with generalized linear constraints,
whereby the data from an array of sensors forms the forcing function. The
solution of the equation is formulated as a least squares (LS) problem with
linear constraints. The LS approach makes the method suitable for the explicit
solution of inverse problems where the forcing function is perturbed by noise.
The algebraic computation is partitioned into a initial preparatory step, which
precomputes the matrices required for the run-time computation; and the cyclic
run-time computation, which is repeated with each acquisition of sensor data.
The cyclic computation consists of a single matrix-vector multiplication, in
this manner computation complexity is known a-priori, fulfilling the definition
of a real-time computation. Numerical testing of the new method is presented on
perturbed as well as unperturbed problems; the results are compared with known
analytic solutions and solutions acquired from state-of-the-art implicit
solvers. The solution is implemented with model based design and uses only
fundamental linear algebra; consequently, this approach supports automatic code
generation for deployment on embedded systems. The targeting concept was tested
via software- and processor-in-the-loop verification on two systems with
different processor architectures. Finally, the method was tested on a
laboratory prototype with real measurement data for the monitoring of flexible
structures. The problem solved is: the real-time overconstrained reconstruction
of a curve from measured gradients. Such systems are commonly encountered in
the monitoring of structures and/or ground subsidence.Comment: 24 pages, journal articl
Starting step size for an ODE solver
AbstractOne of the more critical issues in solving ordinary differential equations by a step-by-step process occurs in the starting phase. Somehow the procedure must be supplied with an initial step size that is on scale for the problem at hand. It must be small enough to yield a reliable solution by the process, but not so small as to significantly affect the efficiency of solution. In this paper, we discuss an algorithm for obtaining a good starting step size and present a subroutine which can be readily used in most ODE solvers
Calibrated Adaptive Probabilistic ODE Solvers
Probabilistic solvers for ordinary differential equations assign a posterior
measure to the solution of an initial value problem. The joint covariance of
this distribution provides an estimate of the (global) approximation error. The
contraction rate of this error estimate as a function of the solver's step size
identifies it as a well-calibrated worst-case error, but its explicit numerical
value for a certain step size is not automatically a good estimate of the
explicit error. Addressing this issue, we introduce, discuss, and assess
several probabilistically motivated ways to calibrate the uncertainty estimate.
Numerical experiments demonstrate that these calibration methods interact
efficiently with adaptive step-size selection, resulting in descriptive, and
efficiently computable posteriors. We demonstrate the efficiency of the
methodology by benchmarking against the classic, widely used Dormand-Prince 4/5
Runge-Kutta method.Comment: 17 pages, 10 figures
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