3,001 research outputs found
POD‐identification reduced order model of linear transport equations for control purposes
Intrusive reduced order modeling techniques require access to the solver's discretization and solution algorithm, which are not available for most computational fluid dynamics codes. Therefore, a nonintrusive reduction method that identifies the system matrix of linear fluid dynamical problems with a least-squares technique is presented. The methodology is applied to the linear scalar transport convection-diffusion equation for a 2D square cavity problem with a heated lid. The (time-dependent) boundary conditions are enforced in the obtained reduced order model (ROM) with a penalty method. The results are compared and the accuracy of the ROMs is assessed against the full order solutions and it is shown that the ROM can be used for sensitivity analysis by controlling the nonhomogeneous Dirichlet boundary conditions
An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
The movement of many organisms can be described as a random walk at either or
both the individual and population level. The rules for this random walk are
based on complex biological processes and it may be difficult to develop a
tractable, quantitatively-accurate, individual-level model. However, important
problems in areas ranging from ecology to medicine involve large collections of
individuals, and a further intellectual challenge is to model population-level
behavior based on a detailed individual-level model. Because of the large
number of interacting individuals and because the individual-level model is
complex, classical direct Monte Carlo simulations can be very slow, and often
of little practical use. In this case, an equation-free approach may provide
effective methods for the analysis and simulation of individual-based models.
In this paper we analyze equation-free coarse projective integration. For
analytical purposes, we start with known partial differential equations
describing biological random walks and we study the projective integration of
these equations. In particular, we illustrate how to accelerate explicit
numerical methods for solving these equations. Then we present illustrative
kinetic Monte Carlo simulations of these random walks and show a decrease in
computational time by as much as a factor of a thousand can be obtained by
exploiting the ideas developed by analysis of the closed form PDEs. The
illustrative biological example here is chemotaxis, but it could be any random
walker which biases its movement in response to environmental cues.Comment: 30 pages, submitted to Physica
A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures
In this paper, we develop a nested hybridizable discontinuous Galerkin (HDG)
method to numerically solve the Maxwell's equations coupled with the
hydrodynamic model for the conduction-band electrons in metals. By means of a
static condensation to eliminate the degrees of freedom of the approximate
solution defined in the elements, the HDG method yields a linear system in
terms of the degrees of freedom of the approximate trace defined on the element
boundaries. Furthermore, we propose to reorder these degrees of freedom so that
the linear system accommodates a second static condensation to eliminate a
large portion of the degrees of freedom of the approximate trace, thereby
yielding a much smaller linear system. For the particular metallic structures
considered in this paper, the resulting linear system obtained by means of
nested static condensations is a block tridiagonal system, which can be solved
efficiently. We apply the nested HDG method to compute the second harmonic
generation (SHG) on a triangular coaxial periodic nanogap structure. This
nonlinear optics phenomenon features rapid field variations and extreme
boundary-layer structures that span multiple length scales. Numerical results
show that the ability to identify structures which exhibit resonances at
and is paramount to excite the second harmonic response.Comment: 31 pages, 7 figure
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