229,599 research outputs found
A posteriori modeling error estimates in the optimization of two-scale elastic composite materials
The a posteriori analysis of the discretization error and the modeling error
is studied for a compliance cost functional in the context of the optimization
of composite elastic materials and a two-scale linearized elasticity model. A
mechanically simple, parametrized microscopic supporting structure is chosen
and the parameters describing the structure are determined minimizing the
compliance objective. An a posteriori error estimate is derived which includes
the modeling error caused by the replacement of a nested laminate
microstructure by this considerably simpler microstructure. Indeed, nested
laminates are known to realize the minimal compliance and provide a benchmark
for the quality of the microstructures. To estimate the local difference in the
compliance functional the dual weighted residual approach is used. Different
numerical experiments show that the resulting adaptive scheme leads to simple
parametrized microscopic supporting structures that can compete with the
optimal nested laminate construction. The derived a posteriori error indicators
allow to verify that the suggested simplified microstructures achieve the
optimal value of the compliance up to a few percent. Furthermore, it is shown
how discretization error and modeling error can be balanced by choosing an
optimal level of grid refinement. Our two scale results with a single scale
microstructure can provide guidance towards the design of a producible
macroscopic fine scale pattern
Towards the efficient calculation of quantity of interest from steady Euler equations II: a CNNs-based automatic implementation
In \cite{wang2023towards}, a dual-consistent dual-weighted residual-based
-adaptive method has been proposed based on a Newton-GMG framework, towards
the accurate calculation of a given quantity of interest from Euler equations.
The performance of such a numerical method is satisfactory, i.e., the stable
convergence of the quantity of interest can be observed in all numerical
experiments. In this paper, we will focus on the efficiency issue to further
develop this method, since efficiency is vital for numerical methods in
practical applications such as the optimal design of the vehicle shape. Three
approaches are studied for addressing the efficiency issue, i.e., i). using
convolutional neural networks as a solver for dual equations, ii). designing an
automatic adjustment strategy for the tolerance in the -adaptive process to
conduct the local refinement and/or coarsening of mesh grids, and iii).
introducing OpenMP, a shared memory parallelization technique, to accelerate
the module such as the solution reconstruction in the method. The feasibility
of each approach and numerical issues are discussed in depth, and significant
acceleration from those approaches in simulations can be observed clearly from
a number of numerical experiments. In convolutional neural networks, it is
worth mentioning that the dual consistency plays an important role to guarantee
the efficiency of the whole method and that unstructured meshes are employed in
all simulations.Comment: In this papers, we use the CNNs architecture to solve the dual
equations proble
Goal driven optimization of process parameters for maximum efficiency in laser bending of advanced high strength steels
Laser forming or bending is fast becoming an attractive option for the forming of advanced high strength steels (AHSS), due primarily to the reduced formability of AHSS when compared with conventional steels in traditional contact-based forming processes. An inherently iterative process, laser forming must be optimized for efficiency in order to compete with contact based forming processes; as such, a robust and accurate method of optimal process parameter prediction is required. In this paper, goal driven optimization is conducted, utilizing numerical simulations as the basis for the prediction of optimal process parameters for the laser bending of DP 1000 steel. A key consideration of the optimization process is the requirement for minimal microstructural transformation in automotive grade high strength steels such as DP 1000
Composite Dipolar Recoupling: Anisotropy Compensated Coherence Transfer in Solid-State NMR
The efficiency of dipole-dipole coupling driven coherence transfer
experiments in solid-state NMR spectroscopy of powder samples is limited by
dispersion of the orientation of the internuclear vectors relative to the
external magnetic field. Here we introduce general design principles and
resulting pulse sequences that approach full polarization transfer efficiency
for all crystallite orientations in a powder in magic-angle-spinning
experiments. The methods compensate for the defocusing of coherence due to
orientation dependent dipolar coupling interactions and inhomogeneous
radio-frequency fields. The compensation scheme is very simple to implement as
a scaffold (comb) of compensating pulses in which the pulse sequence to be
improved may be inserted. The degree of compensation can be adjusted and should
be balanced as a compromise between efficiency and length of the overall pulse
sequence. We show by numerical and experimental data that the presented
compensation protocol significantly improves the efficiency of known dipolar
recoupling solid-state NMR experiment
Optimal control of transitions between nonequilibrium steady states
Biological systems fundamentally exist out of equilibrium in order to
preserve organized structures and processes. Many changing cellular conditions
can be represented as transitions between nonequilibrium steady states, and
organisms have an interest in optimizing such transitions. Using the
Hatano-Sasa Y-value, we extend a recently developed geometrical framework for
determining optimal protocols so that it can be applied to systems driven from
nonequilibrium steady states. We calculate and numerically verify optimal
protocols for a colloidal particle dragged through solution by a translating
optical trap with two controllable parameters. We offer experimental
predictions, specifically that optimal protocols are significantly less costly
than naive ones. Optimal protocols similar to these may ultimately point to
design principles for biological energy transduction systems and guide the
design of artificial molecular machines.Comment: Accepted for publication at PLoS ON
Non-local control in the conduction coefficients: well posedness and convergence to the local limit
We consider a problem of optimal distribution of conductivities in a system
governed by a non-local diffusion law. The problem stems from applications in
optimal design and more specifically topology optimization. We propose a novel
parametrization of non-local material properties. With this parametrization the
non-local diffusion law in the limit of vanishing non-local interaction
horizons converges to the famous and ubiquitously used generalized Laplacian
with SIMP (Solid Isotropic Material with Penalization) material model. The
optimal control problem for the limiting local model is typically ill-posed and
does not attain its infimum without additional regularization. Surprisingly,
its non-local counterpart attains its global minima in many practical
situations, as we demonstrate in this work. In spite of this qualitatively
different behaviour, we are able to partially characterize the relationship
between the non-local and the local optimal control problems. We also
complement our theoretical findings with numerical examples, which illustrate
the viability of our approach to optimal design practitioners
- …