Analysis of preconditioned Picard iterations for the Navier-Stokes equations

Mixed finite element formulations of fluid flow problems lead to large systems of equations of saddle-point type for which iterative solution methods are mandatory for reasons of efficiency. A successful approach in the design of solution methods takes into account the structure of the problem; in particular, it is well-known that an efficient solution can be obtained if the associated Schur complement problem can be solved efficiently and robustly. In this work we analyze a preconditioner for the Schur complement for the Oseen problem which was introduced in Numerical Analysis Report No. 99/06 We show that the spectrum of the preconditioned system is independent of the mesh parameter; moreover, we demonstrate that the number of GMRES iterations grows like the square-root of the Reynolds number for steady-state problems, while for time-dependent problems this dependence becomes negligible. In both the steady-state and time-dependent case the performance is mesh-independent

Constraint interface preconditioning for topology optimization problems

The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity and size. In this work we propose a methodology which brings together existing fast algorithms, namely, interior-point for the optimization problem and a novel substructuring domain decomposition method for the ensuing large-scale linear systems. The main contribution is the choice of interface preconditioner which allows for the acceleration of the domain decomposition method, leading to performance independent of problem size.Comment: To be published in SIAM J. Sci. Com

Satisfaction assessment of patient with idiopathic inflammatory myopathies according to the PSQ-III questionnaire: cross-sectional study

Disciplina medicină internă-semiologie, Departamentul de medicină internă, Universitatea de Stat de Medicină şi Farmacie „Nicolae Testemiţanu”, Chișinău, Republica MoldovaRezumat. Introducere. Miopatiile inflamatorii idiopatice (MII), reprezintă un grup eterogen de maladii autoimune rare, caracterizate prin slăbiciune musculară proximală, simetrică, lent-progresivă și fatigabilitate. Dat fiind faptul că miopatiile inflamatorii idiopatice sunt boli cronice cu implicare multiorganică, ce rezultă în numeroase consecințe și la care se asociază comorbidități, acești pacienți necesită o atenție sporită din partea medicilor ca timp și resurse medicale. Satisfacția pacienților este o noțiune complexă, fiind determinată de multiple variabile așa ca organizarea serviciilor de sănătate, dotarea tehnică a instituțiilor medicale dar, nu în ultimul rând, de abilitățile de comunicare, respect, explicații și informații clare, care sunt mai esențiale decât competențele tehnice ale personalului medical. Percepțiile pacienților, la rândul lor, sunt influențate de statutul socio-cultural, convingerile lor, atitudinile și nivelul lor de înțelegere. Material şi metode. A fost efectuat un studiu transversal, în cadrul Departamentului de medicină internă, Disciplina medicină internă-semiologie a Universităţii de Stat de Medicină şi Farmacie „Nicolae Testemiţanu’’ din Republica Moldova, la baza clinică a Institutului de Cardiologie, în perioada mai 2016 - septembrie 2018. În cadrul studiului, au fost incluși 67 de pacienţi cu MII, conform criteriilor de clasificare ACR/ EULAR 2017. Ulterior, pacienții cercetați au fost divizați în 2 loturi, în funcție de durata bolii: lotul <2 ani și lotul ≥2 ani. Gradul satisfacției pacienților faţă de serviciile medicale acordate a fost determinat prin utilizarea chestionarului Patient Satisfaction Questionnaire (PSQ-III), varianta III. Rezultate. Vârsta medie la momentul cercetării a constituit 53,1±12,5 ani, cu o durată medie a bolii de 99,1±72,6 luni. În lotul de studiu au predominat femeile, cu un raport femei:bărbați de 3,2:1. Nivelul educațional superior a prevalat atât în lotul <2 ani, cât și lotul ≥2 ani. Angajarea în câmpul muncii constatată la pacienții din lotul <2 ani a fost cu precădere prin angajare cu normă întreagă și persoane pensionate în baza atingerii vârstei de pensionare, versus în lotul ≥2 ani – persoane pensionate în baza atingerii vârstei de pensionare. La aplicarea chestionarului PSQ-III, a fost determinat un nivel al satisfacției redus față de media populației generale pe parcursul tuturor domeniilor, în ambele loturi. De asemenea, nu s-au identificat diferențe statistic semnificative între rezultatele pe domenii ale celor 2 loturi. Concluzii. Nivelul de satisfacție al pacienților cu miopatii inflamatorii idiopatice este redus, cele mai mici scoruri au fost pe domeniul de aspecte financiare, vizavi de scoruri mai mari la domeniul comunicare. Gradul de satisfacție pare sa nu fie influențat de durata bolii.Abstract. Introduction. Idiopathic inflammatory myopathies (IIM) represent a heterogeneous group of rare autoimmune diseases characterized by proximal, symmetrical, slow-progressive muscle weakness and fatigue. Given that idiopathic inflammatory myopathies are chronic diseases with multi-organic involvement that result in many consequences and associated with comorbidities, these patients require increased attention from physicians as time and medical resources. Patient satisfaction is a complex notion that is determined by multiple variables such as the organization of health services, the technical endowment of medical institutions, but not least the clear communication skills, respect, explanations and information that are more essential and also technical skills of the medical staff. Patient perceptions are influenced by their socio-cultural status, beliefs, attitudes and level of understanding. Material and methods. A cross-sectional study was conducted in the Department of internal medicine, Department of internal medicine and semiology of Nicolae Testemitanu State University of Medicine and Pharmacy of the Republic of Moldova, at the clinical base of the Institute of Cardiology, between May 2016 and September 2018. There were 67 patients with MII included in the study according to the ACR/ EULAR 2017 classification criteria. Subsequently, the investigated patients were divided into two groups depending on the duration of the disease, lot <2 years and lot ≥2 years. Patient satisfaction with medical services was determined using the Patient Satisfaction Questionnaire (PSQ III) version III. Results. The mean age at the time of the study was 53.1±12.5 years, mean disease duration was 99.1±72.6 months. Women prevailed in the study group with a 3.2:1 female: male ratio. The higher education level prevailed in both groups. The employment rate found among patients in the group <2 year was mainly by full-time employment and retired people versus in the group ≥2 years – retired people due to retirement age. Obtained scores at the application of PSQ-III questionnaire were lower than those of general population across all domains in both groups. Also, no statistically significant differences were found between the field results of the two lots. Conclusions. The level of satisfaction determined in patients with idiopathic inflammatory myopathies was reduced, the lowest scores were in the financial aspects subscale and highest in the communication domain. The degree of satisfaction does not seem to be influenced by the duration of the disease

Expresia consecințelor miopatiilor inflamatorii idiopatice

321.04 - Rheumatology Summary of Doctoral Thesis in Medical Sciences[...] THE CONCEPTUAL RESEARCH ITEMS Topicality. The holistic and complex approach of patients with idiopathic inflammatory myopathies (IIM) involves examining, from the perspective of disease activity, the organic damage and the quality of life, components that influence each other. Although IIMs are regarded as treatable conditions, their prognosis is not well known, therefore the disease outcomes available in the literature and prognostic factors vary greatly due to methodological imperfections [1,13].[...][...] REPERELE CONCEPTUALE ALE CERCETĂRII Actualitatea temei. Abordarea holistică și complexă a pacienților cu miopatii inflamatorii idiopatice (MII) presupune examinarea prin prisma activității bolii, lezării organice și calității vieții, componente ce se influențează reciproc. Cu toate că MII sunt considerate afecțiuni ce se supun tratamentului, prognosticul nu este bine cunoscut, în literatura de specialitate consecințele bolii și factorii de prognostic variază foarte mult datorită imperfecțiunilor metodologice 1,13. [...

A Green's function preconditioner for the steady-state Navier-Stokes equations

In this paper we present an efficient method for solving the sparse linear system of equations arising from the discretization of the linearised steady-state Navier-Stokes equations (also known as the Oseen equations). The solver is an iterative method of Krylov subspace type for which we devise a preconditioner based on Green's tensor for the Oseen operator. The preconditioner supersedes existing preconditioners for the Oseen problem in that it exhibits only a mild dependence on the viscosity (inverse Reynolds number) and, most importantly, improved performance with the size of the problem. This comes as no surprise, as preconditioners based on the continuous inverse are expected to perform better on discretizations which approximate well the continuous operator

Analysis of preconditioners for saddle-point problems

Mixed finite element formulations give rise to large, sparse, block linear systems of equations the solution of which is often sought via a preconditioned iterative technique. In this work we present a general analysis of block-preconditioners based on the stability conditions inherited from the formulation of the finite element method (the Babuska-Brezzi, or inf-sup conditions)

Preconditioning the Advection-Diffusion Equation: the Green's Function Approach

We look at the relationship between efficient preconditioners (i.e., good approximations to the discrete inverse operator) and the generalized inverse for the (continuous) advection-diffusion operator -- the Green's function. We find that the continuous Green's function exhibits two important properties -- directionality and rapid downwind decay -- which are preserved by the discrete (grid) Green's functions, if and only if the discretization used produces non-oscillatory solutions. In particular, the downwind decay ensures the locality of the grid Green's functions. Hence, a finite element formulation which produces a good solution will typically use a coefficient matrix with almost lower triangular structure under a "with-the-flow" numbering of the variables. It follows that the block Gauss-Seidel matrix is a first candidate for a preconditioner to use with an iterative solver of Krylov subspace type

A preconditioner for the 3D Oseen equations

We describe a preconditioner for the linearised incompressible Navier-Stokes equations (the Oseen equations) which requires as components only a preconditioner/solver for each of a discrete Laplacian and a discrete advection-diffusion operator. With this preconditioner, convergence of an iterative method such as GMRES is independent of the mesh size and depends only mildly on the viscosity parameter (the inverse Reynolds number). Thus when the component preconditioner/solvers are effective on their respective subproblems (as one expects with an appropriate multigrid cycle for instance) a fast Oseen solver results