4,432 research outputs found
An isogeometric analysis for elliptic homogenization problems
A novel and efficient approach which is based on the framework of
isogeometric analysis for elliptic homogenization problems is proposed. These
problems possess highly oscillating coefficients leading to extremely high
computational expenses while using traditional finite element methods. The
isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in
this paper is regarded as an alternative approach to the standard Finite
Element Heterogeneous Multiscale Method (FE-HMM) which is currently an
effective framework to solve these problems. The method utilizes non-uniform
rational B-splines (NURBS) in both macro and micro levels instead of standard
Lagrange basis. Beside the ability to describe exactly the geometry, it
tremendously facilitates high-order macroscopic/microscopic discretizations
thanks to the flexibility of refinement and degree elevation with an arbitrary
continuity level provided by NURBS basis functions. A priori error estimates of
the discretization error coming from macro and micro meshes and optimal micro
refinement strategies for macro/micro NURBS basis functions of arbitrary orders
are derived. Numerical results show the excellent performance of the proposed
method
Interference Exploitation-based Hybrid Precoding with Robustness Against Phase Errors
Hybrid analog-digital precoding significantly reduces the hardware costs in
massive MIMO transceivers when compared to fully-digital precoding at the
expense of increased transmit power. In order to mitigate the above shortfall,
we use the concept of constructive interference-based precoding, which has been
shown to offer significant transmit power savings when compared with the
conventional interference suppression-based precoding in fully-digital
multiuser MIMO systems. Moreover, in order to circumvent the potential
quality-of-service degradation at the users due to the hardware impairments in
the transmitters, we judiciously incorporate robustness against such
vulnerabilities in the precoder design. Since the undertaken constructive
interference-based robust hybrid precoding problem is nonconvex with infinite
constraints and thus difficult to solve optimally, we decompose the problem
into two subtasks, namely, analog precoding and digital precoding. In this
paper, we propose an algorithm to compute the optimal constructive
interference-based robust digital precoders. Furthermore, we devise a scheme to
facilitate the implementation of the proposed algorithm in a low-complexity and
distributed manner. We also discuss block-level analog precoding techniques.
Simulation results demonstrate the superiority of the proposed algorithm and
its implementation scheme over the state-of-the-art methods
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
Computational Engineering
The focus of this Computational Engineering Workshop was on the mathematical foundation of state-of-the-art and emerging finite element methods in engineering analysis. The 52 participants included mathematicians and engineers with shared interest on discontinuous Galerkin or Petrov-Galerkin methods and other generalized nonconforming or mixed finite element methods
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