769 research outputs found
Coupling problem in thermal systems simulations
Building energy simulation is playing a key role in building design in order to reduce the energy
consumption and, consequently, the CO2 emissions. An object-oriented tool called NEST
is used to simulate all the phenomena that appear in a building. In the case of energy and momentum
conservation and species transport, the current solver behaves well, but in the case of
mass conservation it takes a lot of time to reach a solution. For this reason, in this work, instead
of solving the continuity equations explicitly, an implicit method based on the Trust Region algorithm
is proposed. Previously, a study of the properties of the model used by NEST-Building
software has been done in order to simplify the requirements of the solver. For a building with
only 9 rooms the new solver is a thousand times faster than the current method
Enhancing structure relaxations for first-principles codes: an approximate Hessian approach
We present a method for improving the speed of geometry relaxation by using a
harmonic approximation for the interaction potential between nearest neighbor
atoms to construct an initial Hessian estimate. The model is quite robust, and
yields approximately a 30% or better reduction in the number of calculations
compared to an optimized diagonal initialization. Convergence with this
initializer approaches the speed of a converged BFGS Hessian, therefore it is
close to the best that can be achieved. Hessian preconditioning is discussed,
and it is found that a compromise between an average condition number and a
narrow distribution in eigenvalues produces the best optimization.Comment: 9 pages, 3 figures, added references, expanded optimization sectio
Geometrical inverse preconditioning for symmetric positive definite matrices
We focus on inverse preconditioners based on minimizing , where is the preconditioned matrix
and is symmetric and positive definite. We present and analyze
gradient-type methods to minimize
on a suitable compact set. For that we use the geometrical properties of the
non-polyhedral
cone of symmetric and positive definite matrices, and also the special
properties of on the feasible set.
Preliminary and encouraging numerical results are also presented
in which dense and sparse approximations are included
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