Recycling BiCGSTAB with an Application to Parametric Model Order Reduction

Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique, the recycling BiCG algorithm has been developed recently. Here, we now generalize and extend this recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving sequences of dual linear systems, while the focus here is on efficiently solving sequences of single linear systems (assuming non-symmetric matrices for both recycling BiCG and recycling BiCGSTAB). As compared with other methods for solving sequences of single linear systems with non-symmetric matrices (e.g., recycling variants of GMRES), BiCG based recycling algorithms, like recycling BiCGSTAB, have the advantage that they involve a short-term recurrence, and hence, do not suffer from storage issues and are also cheaper with respect to the orthogonalizations. We modify the BiCGSTAB algorithm to use a recycle space, which is built from left and right approximate invariant subspaces. Using our algorithm for a parametric model order reduction example gives good results. We show about 40% savings in the number of matrix-vector products and about 35% savings in runtime.Comment: 18 pages, 5 figures, Extended version of Max Planck Institute report (MPIMD/13-21

O-MOORE-NICE!: new methodologies and algorithms for design and simulation of analog integrated circuits

No abstract

Dimensions of Entrepreneurial Orientation in the Academic Environment

The establishment of entrepreneurial orientation (EO) in the academic environment, through its basilar conceptual dimensions such as proactiveness, innovativeness, and risk-taking, has been the subject of relevant debate for academics, higher education managers, and policy-makers. In this context, this article aims to analyze the establishment of EO in the academic environment, pursuing an entrepreneurial university model. Thus, the strategy of multiple case studies was adopted, based on three universities: two in Brazil, the Pontifical Catholic University of Rio Grande do Sul (PUC-RS) and the Pontifical Catholic University of Rio de Janeiro (PUC-Rio), and one in Sweden, the Lund University (LU). Results show that the EO established by the universities studied is seen in several times and in different ways through its conceptual dimensions, suitable to the academic context. The movements observed in the three cases researched show non-sporadic behaviors towards an entrepreneurial university model over time

Fast A Posteriori State Error Estimation for Reliable Frequency Sweeping in Microwave Circuits via the Reduced-Basis Method

We develop a compact, reliable model order reduction approach for fast frequency sweeps in microwave circuits by means of the reduced-basis method. Contrary to what has been previously done, special emphasis is placed on certifying the accuracy of the reduced-order model with respect to the original full-order model in an effective and efficient way. Previous works on model order reduction accuracy certification rely on costly $\textit{a posteriori}$ error estimators, which typically require expensive $\textit{inf-sup}$ constant evaluations of the underlying full-order model. This scenario is often too time-consuming and unaffordable in electromagnetic applications. As a result, less expensive and heuristic error estimators are commonly used instead. Very often, one is interested in knowing about the full state vector, instead of just some output quantities derived from the full state. Therefore, error estimators for the full state vector become relevant. In this work, we detail the frequency behavior of both the electric field and the state error when an approximation to the electric field solution is carried out. Both field quantities share the same frequency behavior. Based on this observation, we focus on the efficient estimation of the electric field state error and propose a fast evaluation of the reduced-order model state error in the frequency band of analysis, minimizing the number of full-order model evaluations. This methodology is of paramount importance to carry out a reliable fast frequency sweep in microwave circuits. Finally, real-life applications will illustrate the capabilities and efficiency of the proposed approach.Comment: 24 pages, 13 Figures, 6 Table

Adaptive Interpolatory MOR by Learning the Error Estimator in the Parameter Domain

Interpolatory methods offer a powerful framework for generating reduced-order models (ROMs) for non-parametric or parametric systems with time-varying inputs. Choosing the interpolation points adaptively remains an area of active interest. A greedy framework has been introduced in Feng et al. [ESAIM: Math. Model. Numer. Anal. 51(6), 2017] and in Feng and Benner [IEEE Trans. Microw. Theory Techn. 67(12), 2019] to choose interpolation points automatically using a posteriori error estimators. Nevertheless, when the parameter range is large or if the parameter space dimension is larger than two, the greedy algorithm may take considerable time, since the training set needs to include a considerable number of parameters. As a remedy, we introduce an adaptive training technique by learning an efficient a posteriori error estimator over the parameter domain. A fast learning process is created by interpolating the error estimator using radial basis functions (RBF) over a fine parameter training set, representing the whole parameter domain. The error estimator is evaluated only on a coarse training set including a few parameter samples. The algorithm is an extension of the work in Chellappa et al. [arXiv e-prints 1910.00298] to interpolatory model order reduction (MOR) in frequency domain. Beyond this work, we use a newly proposed inf-sup-constant-free error estimator in the frequency domain, which is often much tighter than the error estimator using the inf-sup constant.Comment: 21 pages, 6 figures, 3 tables. Submitted to the proceedings of MODRED 201

Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric Systems in Electromagnetics

A reliable model order reduction process for parametric analysis in electromagnetics is detailed. Special emphasis is placed on certifying the accuracy of the reduced-order model. For this purpose, a sharp state error estimator is proposed. Standard a posteriori state error estimation for model order reduction relies on the inf-sup constant. For parametric systems, the inf-sup constant is parameter-dependent. The a posteriori error estimation for systems with very small or vanishing inf-sup constant poses a challenge, since it is inversely proportional to the inf-sup constant, resulting in rather useless, overly pessimistic error estimators. Such systems appear in electromagnetics since the inf-sup constant values are close to zero at points close to resonant frequencies, where they eventually vanish. We propose a novel a posteriori state error estimator which avoids the calculation of the inf-sup constant. The proposed state error estimator is compared with the standard error estimator and a recently proposed one in the literature. It is shown that our proposed error estimator outperforms both existing estimators. Numerical experiments are performed on real-life microwave devices such as narrowband and wideband antennas, as well as a dual-mode waveguide filter. These examples show the capabilities and efficiency of the proposed methodology.Comment: 15 pages, 21 Figures, 2 Table

Application of DETECTER, an evolutionary genomic tool to analyze genetic variation, to the cystic fibrosis gene family

BACKGROUND: The medical community requires computational tools that distinguish missense genetic differences having phenotypic impact within the vast number of sense mutations that do not. Tools that do this will become increasingly important for those seeking to use human genome sequence data to predict disease, make prognoses, and customize therapy to individual patients. RESULTS: An approach, termed DETECTER, is proposed to identify sites in a protein sequence where amino acid replacements are likely to have a significant effect on phenotype, including causing genetic disease. This approach uses a model-dependent tool to estimate the normalized replacement rate at individual sites in a protein sequence, based on a history of those sites extracted from an evolutionary analysis of the corresponding protein family. This tool identifies sites that have higher-than-average, average, or lower-than-average rates of change in the lineage leading to the sequence in the population of interest. The rates are then combined with sequence data to determine the likelihoods that particular amino acids were present at individual sites in the evolutionary history of the gene family. These likelihoods are used to predict whether any specific amino acid replacements, if introduced at the site in a modern human population, would have a significant impact on fitness. The DETECTER tool is used to analyze the cystic fibrosis transmembrane conductance regulator (CFTR) gene family. CONCLUSION: In this system, DETECTER retrodicts amino acid replacements associated with the cystic fibrosis disease with greater accuracy than alternative approaches. While this result validates this approach for this particular family of proteins only, the approach may be applicable to the analysis of polymorphisms generally, including SNPs in a human population

Bioerosion of Lower Ordovician Hardgrounds in Southern Scandinavia and Western North America.

Trace fossils produced by macroboring invertebrates can be found in carbonate hardgrounds of early Ordovician age in southern Sweden, southern Norway and western Utah (U.S.A.). The bioeroded rocks are highly fossiliferous, thinly bedded, shallow-marine li-mestones. The macroborings in each of the three localities are vase-shaped cavities with diameters and lengths ranging from one to a few centimeters. At least some of the Swedish specimens apparently belong to the ichnogenus Gastrochaenolites LEYMERIE. These bioerosion trace fossils appear to be the oldest macroborings in carbonate hardgrounds, and they indicate that the macroboring niche was firmly established in shallow-marine carbonate shelf environments at least by Arenig time in the Ordovician Period