Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations

A short guide to exponential Krylov subspace time integration for Maxwell's equations

The exponential time integration, i.e., time integration which involves the matrix exponential, is an attractive tool for solving Maxwell’s equations in time. However, its application in practice often requires a substantial knowl-edge of numerical linear algebra algorithms, in particular, of the Krylov subspace methods. This note provides a brief guide on how to apply ex-ponential Krylov subspace time integration in practice. Although we con-sider Maxwell’s equations, the guide can readily be used for other similar time-dependent problems. In particular, we discuss in detail the Arnoldi shift-and-invert method combined with recently introduced residual-based stopping criterion. Two of the algorithms described here are available as MATLAB codes and can be downloaded from the websit

Tuberculosis as a potential pitfall on FDG PET/CT in patients with Hodgkin`s lymphoma - a case report

FDG-PET is an essential diagnostic tool in the management of Hodgkin's lymphoma (HD). However, a lot of benign conditions are well-known to present with high FDG uptake thus mimicking malignant activity. Tuberculosis (TBC) is an infection with known high FDG accumulation and should be suspected in patients with lymphoma and those treated with chemotherapy.CASE REPORT: We present a 19-year old female with mediastinal Hodgkins lymphoma who had discrete lung changes on presentation. After initial chemotherapy, patients status worsened, with CT scan showing complete resolution of the mediastinal mass along with progression in the lung. Patient was restaged and mediastinal and lung involvement was proven. Therapy was escalated with further worsening and newly found liver lesions. TBC was clinically suspected although not objectively proven. FDG PET scan revealed high activity infiltrative lung changes, diffuse pleural activity, active liver lesions and celiac lymph nodes. However, changes could not be addressed as malignant, due to TBC or to both. Pleural biopsy revealed TBC. Patient received anti-TBC treatment only. The follow-up FDG PET scan revealed almost complete resolution of all the changes consistent with complete remission of the lymphoma and good treatment response of TBC.CONCLUSION: Based on initial CT report we consider this case a coexistence of TBC and HD at initial presentation with further worsening rather than a newly-developed TBC on an immunosupressed ground. FDG PET is an excellent tool in HD management, but falsely positive results from TBC should be kept in mind, especially when lung in involved.Scripta Scientifica Medica 2013; 45(1): 82-84

Use of 18FFDG PET/CT in Patients with Acute Ischemic Stroke

Introduction: Brain scintigraphy is one of the basic branches of nuclear medicine, which plays an important role in the diagnosis of neurological diseases. Functional neuroimaging techniques involve both SPECT and PET. More widely application found the coregistration of SPECT/CT and SPECT/MRI that integrate functional nuclear medicine with morphological images.Objective: To study the usefulness of (18F)-FDG PET/CT in patients with acute ischemic cerebral stroke.Material and methods: A total of 16 cases (10 males and 6 females, aged between 39 and 80) with acute ischemic cerebral stroke, admitted to First Clinic of Neurology at UMBAL `Sveta Marina` during the period of 2008-2013 year were included in the study. (18F)-FDG PET/CT scans were obtained by means of Phillips Gemini TF machinery, following the corresponding standard protocols. Results: In all patients were visualized hypodense and hypometabolic zones, corresponding to the location of brain infarction and border regions of reduced glucose metabolism, reflecting the so called `penumbra`.Conclusion: Based on the literature data and our own results, we confirm the clinical application of (18F)-FDG PET/CT in patients with acute ischemic strokes. We suggest that this modern method of co-registration might be useful for assessment of structural and metabolic cerebral disorders and possesses an important diagnostic and prognostic significance for the disease outcome