3,530 research outputs found
Parametric Macromodels of Digital I/O Ports
This paper addresses the development of macromodels for input and output ports of a digital device. The proposed macromodels consist of parametric representations that can be obtained from port transient waveforms at the device ports via a well established procedure. The models are implementable as SPICE subcircuits and their accuracy and efficiency are verified by applying the approach to the characterization of transistor-level models of commercial devices
Reduced Order Modeling based Inexact FETI-DP solver for lattice structures
This paper addresses the overwhelming computational resources needed with
standard numerical approaches to simulate architected materials. Those
multiscale heterogeneous lattice structures gain intensive interest in
conjunction with the improvement of additive manufacturing as they offer, among
many others, excellent stiffness-to-weight ratios. We develop here a dedicated
HPC solver that benefits from the specific nature of the underlying problem in
order to drastically reduce the computational costs (memory and time) for the
full fine-scale analysis of lattice structures. Our purpose is to take
advantage of the natural domain decomposition into cells and, even more
importantly, of the geometrical and mechanical similarities among cells. Our
solver consists in a so-called inexact FETI-DP method where the local,
cell-wise operators and solutions are approximated with reduced order modeling
techniques. Instead of considering independently every cell, we end up with
only few principal local problems to solve and make use of the corresponding
principal cell-wise operators to approximate all the others. It results in a
scalable algorithm that saves numerous local factorizations. Our solver is
applied for the isogeometric analysis of lattices built by spline composition,
which offers the opportunity to compute the reduced basis with macro-scale
data, thereby making our method also multiscale and matrix-free. The solver is
tested against various 2D and 3D analyses. It shows major gains with respect to
black-box solvers; in particular, problems of several millions of degrees of
freedom can be solved with a simple computer within few minutes.Comment: 30 pages, 12 figures, 2 table
Non-intrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging
We introduce a new class of integrators for stiff ODEs as well as SDEs. These
integrators are (i) {\it Multiscale}: they are based on flow averaging and so
do not fully resolve the fast variables and have a computational cost
determined by slow variables (ii) {\it Versatile}: the method is based on
averaging the flows of the given dynamical system (which may have hidden slow
and fast processes) instead of averaging the instantaneous drift of assumed
separated slow and fast processes. This bypasses the need for identifying
explicitly (or numerically) the slow or fast variables (iii) {\it
Nonintrusive}: A pre-existing numerical scheme resolving the microscopic time
scale can be used as a black box and easily turned into one of the integrators
in this paper by turning the large coefficients on over a microscopic timescale
and off during a mesoscopic timescale (iv) {\it Convergent over two scales}:
strongly over slow processes and in the sense of measures over fast ones. We
introduce the related notion of two-scale flow convergence and analyze the
convergence of these integrators under the induced topology (v) {\it Structure
preserving}: for stiff Hamiltonian systems (possibly on manifolds), they can be
made to be symplectic, time-reversible, and symmetry preserving (symmetries are
group actions that leave the system invariant) in all variables. They are
explicit and applicable to arbitrary stiff potentials (that need not be
quadratic). Their application to the Fermi-Pasta-Ulam problems shows accuracy
and stability over four orders of magnitude of time scales. For stiff Langevin
equations, they are symmetry preserving, time-reversible and Boltzmann-Gibbs
reversible, quasi-symplectic on all variables and conformally symplectic with
isotropic friction.Comment: 69 pages, 21 figure
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