A local hybrid surrogate‐based finite element tearing interconnecting dual‐primal method for nonsmooth random partial differential equations

A domain decomposition approach for high‐dimensional random partial differential equations exploiting the localization of random parameters is presented. To obtain high efficiency, surrogate models in multielement representations in the parameter space are constructed locally when possible. The method makes use of a stochastic Galerkin finite element tearing interconnecting dual‐primal formulation of the underlying problem with localized representations of involved input random fields. Each local parameter space associated to a subdomain is explored by a subdivision into regions where either the parametric surrogate accuracy can be trusted or where instead one has to resort to Monte Carlo. A heuristic adaptive algorithm carries out a problem‐dependent hp‐refinement in a stochastic multielement sense, anisotropically enlarging the trusted surrogate region as far as possible. This results in an efficient global parameter to solution sampling scheme making use of local parametric smoothness exploration for the surrogate construction. Adequately structured problems for this scheme occur naturally when uncertainties are defined on subdomains, for example, in a multiphysics setting, or when the Karhunen–Loève expansion of a random field can be localized. The efficiency of the proposed hybrid technique is assessed with numerical benchmark problems illustrating the identification of trusted (possibly higher order) surrogate regions and nontrusted sampling regions

A local hybrid surrogate-based finite element tearing interconnecting dual-primal method for nonsmooth random partial differential equations

A domain decomposition approach for high-dimensional random partial differential equations exploiting the localization of random parameters is presented. To obtain high efficiency, surrogate models in multielement representations in the parameter space are constructed locally when possible. The method makes use of a stochastic Galerkin finite element tearing interconnecting dual-primal formulation of the underlying problem with localized representations of involved input random fields. Each local parameter space associated to a subdomain is explored by a subdivision into regions where either the parametric surrogate accuracy can be trusted or where instead one has to resort to Monte Carlo. A heuristic adaptive algorithm carries out a problem-dependent hp-refinement in a stochastic multielement sense, anisotropically enlarging the trusted surrogate region as far as possible. This results in an efficient global parameter to solution sampling scheme making use of local parametric smoothness exploration for the surrogate construction. Adequately structured problems for this scheme occur naturally when uncertainties are defined on subdomains, for example, in a multiphysics setting, or when the Karhunen–Loève expansion of a random field can be localized. The efficiency of the proposed hybrid technique is assessed with numerical benchmark problems illustrating the identification of trusted (possibly higher order) surrogate regions and nontrusted sampling regions. © 2020 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd

Capacity of MIMO Channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high Eb /N0.Peer Reviewe

Performance evaluation of communication systems with transmit diversity

Transmit diversity is a key technique to combat fading with multiple transmit antennae for next-generation wireless communication systems. Space-time block code (STBC) is a main component of this technique. This dissertation consists of four parts: the first three discuss performance evaluation of STBCs in various circumstances, the fourth outlines a novel differential scheme with full transmit diversity. In the first part, closed-form expressions for the bit error rate (BER) are derived for STBC based on Alamouti\u27s scheme and utilizing M-ary phase shift keying (MPSK) modulation. The analysis is carried out for a slow, flat Rayleigh fading channel with coherent detection and with non-coherent differential encoding/decoding. The BER expression for coherent detection is exact. But for differential detection it is an approximation appropriate for a high signal-to-noise ratio. Numerical results are provided for analysis and simulations for BPSK and QPSK modulations. A signal-to-noise ratio loss of approximately 3 dB always occurs with conventional differential detection for STBC compared to coherent detection. In the second part of this dissertation, a multiple-symbol differential detection (MSDD) technique is proposed for MPSK STBCs, which greatly reduces this performance loss by extending the observation interval for decoding. The technique uses maximum likelihood block sequence detection instead of traditional block-by-block detection and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric for an observation interval of N blocks is derived. It is shown that for a moderate number of blocks, MSDD provides more than 1.0 dB performance improvement corresponding to conventional differential detection. In addition, a closed-form pairwise error probability for differential BPSI( STBC is derived for an observation interval of N blocks, and an approximate BER is obtained to evaluate the performance. In the third part, the BER performance of STBC over a spatio-temporal correlated channel with coherent and noncoherent detection is illustrated, where a general space-time correlation model is utilized. The simulation results demonstrate that spatial correlation negatively effects the performance of the STBC scheme with differential detection but temporal correlation positively impacts it. However, with coherent detection, spatial correlation still has negative effect on the performance but temporal correlation has no impact on it. In the final part of this dissertation, a differential detection scheme for DS/CDMA MIMO link is presented. The transmission provides for full transmit and receive diversity gain using a simple detection scheme, which is a natural extension of differential detection combined with an orthogonal transmit diversity (OTD) approach. A capacity analysis for this scheme is illustrated

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90641/1/AIAA-53965-537.pd

Overview of Large-Scale Computing: The Past, the Present, and the Future

published_or_final_versio

Aerodynamic Analyses Requiring Advanced Computers, part 2

Papers given at the conference present the results of theoretical research on aerodynamic flow problems requiring the use of advanced computers. Topics discussed include two-dimensional configurations, three-dimensional configurations, transonic aircraft, and the space shuttle