We examine sub-structuring methods for solving large-scale generalized eigenvalue problems from a purely algebraic point of view. We use the term "algebraic sub-structuring" to refer to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to provide approximate solutions to the original problem. We are interested in the question of which spectral componentsone should extract from each sub-structure in order to produce an approximate solution to the original problem with a desired level of accuracy. Error estimate for the approximation to the small esteigen pair is developed. The estimate leads to a simple heuristic for choosing spectral components (modes) from each sub-structure. The effectiveness of such a heuristic is demonstrated with numerical examples. We show that algebraic sub-structuring can be effectively used to solve a generalized eigenvalue problem arising from the simulation of an accelerator structure. One interesting characteristic of this application is that the stiffness matrix produced by a hierarchical vector finite elements scheme contains a null space of large dimension. We present an efficient scheme to deflate this null space in the algebraic sub-structuring process.

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## Scholarly Works (5 results)

In toroidal magnetic fusion devices, fast-ion D-alpha diagnostic (FIDA) is a powerful method to study the fast-ion feature. The fast-ion characteristics can be inferred from the Doppler shifted spectrum of Dα light according to charge exchange recombination process between fast ions and probe beam. Since conceptual design presented in the last HTPD conference, significant progress has been made to apply FIDA systems on the Experimental Advanced Superconducting Tokamak (EAST). Both co-current and counter-current neutral beam injectors are available, and each can deliver 2-4 MW beam power with 50-80 keV beam energy. Presently, two sets of high throughput spectrometer systems have been installed on EAST, allowing to capture passing and trapped fast-ion characteristics simultaneously, using Kaiser HoloSpec transmission grating spectrometer and Bunkoukeiki FLP-200 volume phase holographic spectrometer coupled with Princeton Instruments ProEM 1024B eXcelon and Andor DU-888 iXon3 1024 CCD camera, respectively. This paper will present the details of the hardware descriptions and experimental spectrum.

### Conceptual design of a fast-ion D-alpha diagnostic on experimental advanced superconducting tokamak.

To investigate the fast ion behavior, a fast ion D-alpha (FIDA) diagnostic system has been planned and is presently under development on Experimental Advanced Superconducting Tokamak. The greatest challenges for the design of a FIDA diagnostic are its extremely low intensity levels, which are usually significantly below the continuum radiation level and several orders of magnitude below the bulk-ion thermal charge-exchange feature. Moreover, an overlaying Motional Stark Effect (MSE) feature in exactly the same wavelength range can interfere. The simulation of spectra code is used here to guide the design and evaluate the diagnostic performance. The details for the parameters of design and hardware are presented.

To investigate the fast ion behavior, a fast ion D-alpha (FIDA) diagnostic system has been installed on EAST. Fast ion features can be inferred from the Doppler shifted spectrum of Balmer-alpha light from energetic hydrogenic atoms. This paper will focus on the validation of FIDA measurements performed using MHD-quiescent discharges in 2015 campaign. Two codes have been applied to calculate the Dα spectrum: one is a Monte Carlo code, Fortran 90 version FIDASIM, and the other is an analytical code, Simulation of Spectra (SOS). The predicted SOS fast-ion spectrum agrees well with the measurement; however, the level of fast-ion part from FIDASIM is lower. The discrepancy is possibly due to the difference between FIDASIM and SOS velocity distribution function. The details will be presented in the paper to primarily address comparisons of predicted and observed spectrum shapes/amplitudes.

© 2015 Elsevier Inc. Glaucoma, a blinding neurodegenerative disease, whose risk factors include elevated intraocular pressure (IOP), age, and genetics, is characterized by accelerated and progressive retinal ganglion cell (RGC) death. Despite decades of research, the mechanism of RGC death in glaucoma is still unknown. Here, we demonstrate that the genetic effect of the SIX6 risk variant (rs33912345, His141Asn) is enhanced by another major POAG risk gene, p16INK4a (cyclin-dependent kinase inhibitor 2A, isoform INK4a). We further show that the upregulation of homozygous SIX6 risk alleles (CC) leads to an increase in p16INK4a expression, with subsequent cellular senescence, as evidenced in a mouse model of elevated IOP and in human POAG eyes. Our data indicate that SIX6 and/or IOP promotes POAG by directly increasing p16INK4a expression, leading to RGC senescence in adult human retinas. Our study provides important insights linking genetic susceptibility to the underlying mechanism of RGC death and provides a unified theory of glaucoma pathogenesis. Zhang et al. report p16INK4a as a downstream integrator of diverse signals, such as inherited genetic risk, age, and intraocular pressure, in the pathogenesis of glaucoma. They demonstrate that upregulation of SIX6 upon stress directly increases p16INK4a, leading to retinal ganglion cell senescence and death.