In this paper, we consider domain decomposition preconditioners for a system of linear algebraic equations arising from the <i>p</i>-version of the fem. We propose several multi-level preconditioners for the Dirichlet problems in the sub-domains in two and three dimensions. It is proved that the condition number of the preconditioned system is bounded by a constant independent of the polynomial degree. The proof uses interpretations of the <i>p</i>-version element stiffness matrix and mass matrix on [-1,1] as <i>h</i>-version stiffness matrix and weighted mass matrix. The analysis requires wavelet methods.

This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.

In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet-Dirichlet domain decomposition pre-conditioner for the system of linear algebraic equations is investigated. The solver for the problem in the sub-domains and a pre-conditioner for the Schur-complement are proposed as ingredients for the inexact DD-pre-conditioner. Finally, several numerical experiments are given.

In this work, prestressed elasticity problem as a model of the so-called glacial isostatic adjustment (GIA) process is studied. The model problem is described by a set of partial differential equations (PDE) and discretized with a mixed finite element (FE) formulation. In the presence of prestress the so-constructed system of equations is non-symmetric and indefinite. Moreover, the resulting system of equations is of the saddle point form. We focus on a robust and efficient block lower-triangular preconditioning method, where the lower diagonal block is and approximation of the so-called Schur complement. The Schur complement is approximated by the so-called element-wise Schur complement. The element-wise Schur complement is constructed by assembling exact local Schur complements on the cell elements and distributing the resulting local matrices to the global preconditioner matrix. We analyse the properties of the element-wise Schur complement for the symmetric indefinite system matrix and provide proof of its quality. We show that the spectral radius of the element-wise Schur complement is bounded by the exact Schur complement and that the quality of the approximation is not affected by the domain shape. The diagonal blocks of the lower-triangular preconditioner are combined with inner iterative schemes accelerated by (numerically) optimal and robust algebraic multigrid (AMG) preconditioner. We observe that on distributed memory systems, the top pivot block of the preconditioner is not scaling satisfactorily. The implementation of the methods is further studied using a general profiling tool, designed for clusters. For nonsymmetric matrices we use the theory of Generalized Locally Toeplitz (GLT) matrices and show the spectral behavior of the element-wise Schur complement, compared to the exact Schur complement. Moreover, we use the properties of the GLT matrices to construct a more efficient AMG preconditioner. Numerical experiments show that the so-constructed methods are robust and optimal.

Abstract During cardiac and aortic surgery, disturbance of the blood supply in the central nervous system occurs when the repair of aortic pathologies is performed or a bloodless operation field is needed in complex cardiac surgery. To enable the suitable operation environment, the technique named hypothermic circulatory arrest (HCA) has been utilized via heart-lung machine. In this method, the core temperature is lowered to the target temperature, after which blood circulation is halted for a certain period of time. A challenge is that the successful usage of HCA, however still involves the risks of postoperative neurological complications and mortality. In cardiac and aortic arch surgery, the brain is at the highest risk for deficits, whereas in the repair of thoracoabdominal aortic aneurysms (TAAAs), spinal cord injury remains the most severe adverse outcome. Adjunctive protective strategies are required to reduce ischemic injury in these settings. In this thesis, Studies I and II focused on the spinal cord and the Study III on the brain. The studies were performed using acute (II, III) or subacute (I) experimental porcine models, primarily aiming to assess the effectiveness of remote ischemic preconditioning (RIPC) in spinal cord protection along with the aim of studying the underlying mechanisms of RIPC in neuroprotection. Studies I and II demonstrated enhanced motor evoked potential (MEP) responses in both hind limbs, indicating spinal cord protection by RIPC. The faster recovery of brain damage marker S100B along with higher cardiac index and lower systemic lactate levels confirmed the cardio- and neuroprotective properties of RIPC in Study III. The protective mechanism of RIPC was associated with increased antioxidant response (II, III). / Tiivistelmä Sydän- ja aorttakirurgiassa, keskushermoston verenkiertoa joudutaan häiritsemään toteutettaessa aortan korjausleikkauksia tai vaikeissa sydänkirurgisissa toimenpiteissä verettömän leikkausalueen saavuttamiseksi. Sydän-keuhkokoneen avulla toteutettava täydellinen verenkierron pysäytys mahdollistaa vaaditut olosuhteet. Tässä menetelmässä ydinlämpötilaa lasketaan ja verenkierron pysäytys toteutaan tavoitellussa kohdelämpötilassa tietyssä aikaikkunassa. Kyseisen menetelmän onnistunut käyttö sisältää kuitenkin riskejä operaatioiden jälkeisiin neurologisiin komplikaatioihin ja kuolleisuuteen. Sydämen ja aortankaaren kirurgiassa aivot ovat suurimmassa vaarassa vaurioille. Rinta- ja vatsa-aortan aneurysmien eli pullistumien korjausleikkauksiin liittyvä selkäydinvaurio on puolestaan yksi vakavimmista ja vaikeimmista seurauksista. Lisäsuojausmenetelmiä tarvitaan vähentämään iskeemistä vauriota näissä asetelmissa. Väitöskirjan osatyöt I ja II keskittyivät selkäytimeen. Osatyö III käsitteli puolestaan aivojen suojausta. Osatyöt toteutettiin akuutteina (II, III) ja subakuutteina (I) kokeellisina porsasmalleina. Tutkimusten tavoitteina oli arvioida esialtistavan perifeerisen raajaiskemian vaikuttavuutta selkäytimen suojauksessa sekä tutkia raajaiskemian taustalla olevia mekanismeja hermokudoksen suojauksessa. Osatöissä I, II havaittiin motoristen herätepotentiaalien parantuneita vasteita molemmissa takajaloissa osoittaen esialtistavan raajaiskemian suojaavan selkäydintä simuloidussa rinta-aortan korjaustoimenpiteessä. Osatyö III keskittyi alhaisessa lämpötilassa toteutettavaan täydelliseen verenkierron pysäytykseen. Tässä tutkimuksessa todetut aivovauriomarkkeri S100B tason nopeampi lasku, korkeampi sydänindeksi ja alhaisemmat laktaattitasot varmistivat raajaiskemian sydän- ja hermokudossuojausvaikutusta. Esialtistavan perifeerisen raajaiskemian suojaava mekanismi voidaan liittää parantuneeseen solujen antioksidanttivasteeseen (II, III).

Abstract Interest in off-pump coronary surgery and ischaemic preconditioning has been increasing. The aim of this study was to evaluate surrogate indicators of haemodynamic, myocardial, and cerebral outcome during off-pump surgery and preconditioning. Haemodynamics and myocardial preservation were monitored in a pilot study of twelve patients undergoing off-pump coronary surgery. Indicators of myocardial metabolism and tissue injury as well as cerebral damage were evaluated in a randomized study of thirty-three patients undergoing on-pump (11) or off-pump surgery with (11) or without (11) preceding myocardial ischaemic preconditioning for five minutes followed by reperfusion for five minutes. The pilot study showed minimal haemodynamic changes and myocardial derangements during off-pump surgery as evaluated intraoperatively based on transcardiac differences of ATP degradation products and lactate and postoperatively based on MB mass of creatine kinase and troponin T. In the following studies, myocardial ischaemic metabolism was evaluated intraoperatively by measuring transcardiac differences of ATP degradation products, lactate, and pH, which increased significantly from the baseline values in all study groups. However, the maximum values of lactate and pH were significantly higher in the cardiopulmonary bypass group (p = 0.02 and p = 0.007, respectively). There were no statistical differences between the preconditioning and non-preconditioning groups. Myocardial tissue injury was evaluated by postoperative leakage of MB mass of creatine kinase and troponin I. Their peak values were significantly higher (p &lt; 0.001 and p = 0.008) after cardiopulmonary bypass (15.1 μg/l and 13.8 μg/l) than after off-pump surgery without preconditioning (6.3 μg/l and 5.2 μg/l). The respective values were 14.8 μg/l and 7.4 μg/l after preconditioning, and there were no statistically significant differences between the off-pump groups with and without preconditioning. Cerebral damage was evaluated based on the intra- and postoperative serum concentrations of neuron-specific enolase, which were corrected with respect to haemolysis. The corrected values were significantly higher after on-pump than off-pump surgery (p = 0.003 and p = 0.005). In conclusion, multi-vessel off-pump coronary artery surgery is a haemodynamically feasible procedure offering better myocardial preservation compared to on-pump surgery. Ischaemic preconditioning of the myocardium does not seem to improve myocardial preservation in off-pump surgery. The slightly lower levels of neuron-specific enolase also suggest less cerebral damage.

This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST's Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.

The method of moment (MoM) [1] is a widely used method in electromagnetics to solve static and dynamic electromagnetic problems on varying geometries. However, in closely spaced geometries coupled with large aspect ratios, e.g. a large parallel plate capacitor with very small separation gap, the problem exhibits several challenges. Firstly, the close proximity of the field and source elements presents problems with convergence in numerical evaluations of the interactions between them. Secondly, the aspect ratio of the geometry gives an approximation whereby to far field points, the source contributions from locations that are far apart appear to cancel each other. This leads to high condition numbers in the system matrix. This thesis explores the potential solution to these problems as well as the application of modular fast and direct (MFD) [2] solver to expedite the solution of such problems.

Anhydrobiotic organisms have the remarkable ability to lose extensive amounts of body water and survive in an ametabolic, suspended animation state. Distributed to various taxa of life, these organisms have evolved strategies to efficiently protect their cell membranes and proteins against extreme water loss. At the molecular level, a variety of mutually non-exclusive mechanisms have been proposed to account particularly for preserving the integrity of the cell membranes in the desiccated state. Recently, it has been shown that the dauer larva of the nematode Caenorhabditis elegans is anhydrobiotic and accumulates high amounts of trehalose during preparation for harsh desiccation (preconditioning), thereby allowing for a reversible desiccation / rehydration cycle. Here, we have used this genetic model to study the biophysical manifestations of anhydrobiosis and show that, in addition to trehalose accumulation, the dauer larvae exhibit a systemic chemical response upon preconditioning by dramatically reducing their phosphatidylcholine (PC) content. The C. elegans strain daf-2 was chosen for these studies, because it forms a constitutive dauer state under appropriate growth conditions. Using complementary approaches such as chemical analysis, time-resolved FTIR-spectroscopy, Langmuir-Blodgett monolayers, and fluorescence spectroscopy, it is shown that this chemical adaptation of the phospholipid (PL) composition has key consequences for their interaction with trehalose. Infrared-spectroscopic experiments were designed and automated to particularly address structural changes during fast hydration transients. Importantly, the coupling of headgroup hydration to acyl chain order at low humidity was found to be altered on the environmentally relevant time scale of seconds. PLs from preconditioned larvae with reduced PC content exhibit a higher trehalose affinity, a stronger hydration-induced gain in acyl chain free volume, and a wider spread of structural relaxation rates during lyotropic transitions and sub- headgroup H-bond interactions as compared to PLs from non-preconditioned larvae. The effects are related to the intrinsically different hydration properties of PC and phosphatidylethanolamine (PE) headgroups, and lead to a larger hydration-dependent rearrangement of trehalose-mediated H-bond network in PLs from preconditioned larvae. This results in a lipid compressibility modulus of ∼0.5 mN/m and 1.2 mN/m for PLs derived from preconditioned and non-preconditioned larvae, respectively. The ensemble of these changes evidences a genetically controlled chemical tuning of the native lipid composition of a true anhydrobiote to functionally interact with a ubiquitous protective disaccharide. The biological relevance of this adaptation is the preservation of plasma membrane integrity by relieving mechanical strain from desiccated trehalose- containing cells during fast rehydration. Finally, the thermo-tropic lipid phase behavior was studied by temperature-dependent ATR-FTIR and fluorescence spectroscopy of LAURDAN-labeled PLs. The results show that the adaptation to drought, which is accomplished to a significant part by the reduction of the PC content, relies on reducing thermo-tropic and enhancing lyotropic phase transitions. The data are interpreted on a molecular level emphasizing the influence of trehalose on the lipid phase transition under biologically relevant conditions by a detailed analysis of the lipid C=O H-bond environment. The salient feature of the deduced model is a dynamic interaction of trehalose at the PL headgroup region. It is proposed here that the location of trehalose is changed from a more peripheral to a more sub-headgroup-associated position. This appears to be particularly pronounced in PLs from preconditioned worms. The sugar slides deeper into the inter-headgroup space during hydration and thereby supports a quick lateral expansion such that membranes can more readily adapt to the volume changes in the swelling biological material at reduced humidity. The data show that the nature of the headgroup is crucial for its interaction with trehalose and there is no general mechanism by which the sugar affects lipidic phase transitions. The intercalation into a phosphatidylethanolamine-rich membrane appears to be unique. In this case, neither the phase transition temperature nor its width is affected by the protective sugar, whereas strong effects on these parameters were observed with other model lipids. With respect to membrane preservation, desiccation tolerance may be largely dependent on reducing phosphatidylcholine and increasing the phsophatidylethanolamine content in order to optimize trehalose headgroup interactions. As a consequence, fast mechanical adaptation of cell membranes to hydration-induced strain can be realized.

Les microphones sont des capteurs qui permettent à nos systèmes électroniques de prendre connaissance de notre environnement acoustique en fournissant un signal électrique représentatif des vibrations de l’air. Ils sont employés dans la plupart des systèmes multimédia, mais aussi dans les appareils auditifs. Dans l’implant auditif, le microphone se substitue à l’oreille humaine capable de détecter des pressions acoustiques variants de quelque μPa à quelques Pa. Les microphones, sont en général accompagnés d’un circuit électronique spécifique qui permet leur exploitation au coeur d’un système hétérogène. Depuis les toutes premières transductions acoustique-électriques, le microphone a été perfectionné avec la mise en oeuvre de nouveau principes de transduction et l’élaboration de circuit de conditionnement plus performants. Dernièrement, l’introduction de la technologie MEMS (Micro Electro Mechanical Systems) a permis de réaliser des microphones extrêmement compacts et peu couteux. Ces travaux de recherches concernent la réalisation d’un circuit électronique dédié à l’exploitation d’un transducteur M&NEMS (Micro & Nano Electro Mechanical Systems) survenant comme une évolution du MEMS. Pour commencer l’étude, le principe de transduction et l’application du microphone sont étudiés. Les circuits existants sont examinés en détail et adaptés au transducteur M&NEMS. Les résultats potentiels sont discutés et situés dans l’application. Dans un second temps, un circuit de conditionnement spécifique est proposé. Les résultats sont présentés puis le circuit électronique dédié est intégré sur silicium. Les performances des blocs fonctionnels intégrés sont mesurées et présentées. / Microphones are sensors which allow gauging acoustic environment through an electric representation of vibrations in the air. They can be found in most multimedia equipment and in hearing aids. In this particular application, microphone substitutes a human ear which is able to sense pressure level of sound ranging from a μPa to few Pa. The read-out circuit of microphones converts physical signal from transducer into electronic signals that can be used in any heterogeneous system involving audio processing. Transducers of microphones have known successive generation of improvement. The latest refinement is related to the emergence of MEMS (Micro Electro Mechanical Systems) technology which is suitable to build compact sensor. This thesis explores the design of a readout-circuit using an innovative M&NEMS (Micro & Nano Electro Mechanical Systems) technology derived from MEMS. The thesis is structured beginning with review of existing circuits for M&NEMS microphone. A comparative study is reported considering the proposed technical specifications using simulations and a prototype was realized using discrete components. In the second phase, an innovative circuit was proposed as an ASIC solution targeting M&NEMS technology developed at CEA-LETI. The performance evaluation and the physical measurements of the proposed ASIC are detailed.