PMID- 26698717
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20160421
LR  - 20181023
IS  - 1094-4087 (Electronic)
IS  - 1094-4087 (Linking)
VI  - 23
IP  - 24
DP  - 2015 Nov 30
TI  - Efficient uncertainty quantification of large two-dimensional optical systems 
      with a parallelized stochastic Galerkin method.
PG  - 30833-50
LID - 10.1364/OE.23.030833 [doi]
AB  - It is well-known that geometrical variations due to manufacturing tolerances can 
      degrade the performance of optical devices. In recent literature, polynomial 
      chaos expansion (PCE) methods were proposed to model this statistical behavior. 
      Nonetheless, traditional PCE solvers require a lot of memory and their 
      computational complexity leads to prohibitively long simulation times, making 
      these methods non-tractable for large optical systems. The uncertainty 
      quantification (UQ) of various types of large, two-dimensional lens systems is 
      presented in this paper, leveraging a novel parallelized Multilevel Fast 
      Multipole Method (MLFMM) based Stochastic Galerkin Method (SGM). It is 
      demonstrated that this technique can handle large optical structures in 
      reasonable time, e.g., a stochastic lens system with more than 10 million 
      unknowns was solved in less than an hour by using 3 compute nodes. The SGM, which 
      is an intrusive PCE method, guarantees the accuracy of the method. By conjunction 
      with MLFMM, usage of a preconditioner and by constructing and implementing a 
      parallelized algorithm, a high efficiency is achieved. This is demonstrated with 
      parallel scalability graphs. The novel approach is illustrated for different 
      types of lens system and numerical results are validated against a collocation 
      method, which relies on reusing a traditional deterministic solver. The last 
      example concerns a Cassegrain system with five random variables, for which a 
      speed-up of more than 12x compared to a collocation method is achieved.
FAU - Zubac, Z
AU  - Zubac Z
FAU - Fostier, J
AU  - Fostier J
FAU - De Zutter, D
AU  - De Zutter D
FAU - Vande Ginste, D
AU  - Vande Ginste D
LA  - eng
PT  - Journal Article
PL  - United States
TA  - Opt Express
JT  - Optics express
JID - 101137103
EDAT- 2015/12/25 06:00
MHDA- 2015/12/25 06:01
CRDT- 2015/12/25 06:00
PHST- 2015/12/25 06:00 [entrez]
PHST- 2015/12/25 06:00 [pubmed]
PHST- 2015/12/25 06:01 [medline]
AID - 332590 [pii]
AID - 10.1364/OE.23.030833 [doi]
PST - ppublish
SO  - Opt Express. 2015 Nov 30;23(24):30833-50. doi: 10.1364/OE.23.030833.