Formulation and analysis of a Schur complement method for fluid-structure interaction

This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully discrete formulations are well-posed. To derive a partitioned scheme, a Schur complement equation, which implicitly expresses the Lagrange multiplier and the fluid pressure in terms of the fluid velocity and structural displacement, is constructed based on the monolithic FSI system. Solving the Schur complement system at each time step allows for the decoupling of the fluid and structure subproblems, making the method non-iterative between subdomains. We investigate bounds for the condition number of the Schur complement matrix and present initial numerical results to demonstrate the performance of our approach, which attains the expected convergence rates.Comment: 27 pages, 4 figure

Lactated Ringer versus albumin in early sepsis therapy (the RASP study): a randomized clinical trial

Introdução: Nos últimos anos, o uso de albumina para ressuscitação nos pacientes com sepse tem se mostrado controverso. O objetivo deste estudo foi avaliar os efeitos da administração de uma solução de albumina em cristaloide (Ringer lactato comparada a uma solução cristaloide (Ringer lactato) em pacientes com câncer e sepse. Local: Unidade de Terapia Intensiva do Instituto do Câncer do Estado de São Paulo, Brasil. Métodos: Estudo unicêntrico, randomizado, duplo-cego, controlado, entre outubro de 2014 e dezembro de 2016. Pacientes com câncer e sepse grave ou choque séptico foram aleatoriamente alocados para receber infusão intravenosa de bolus de 500 mL de albumina a 4% ou solução de cristaloide (Ringer lactato) durante as 6 primeiras horas da ressuscitação volêmica. O desfecho primário foi definido como morte por qualquer causa em 7 dias. Desfecho primário: taxa de mortalidade em 7 dias. Desfechos secundários: morte por qualquer causa em 28 dias, escore de SOFA (sequence organ failur eassessment) em 7 dias, necessidade de ventilação mecânica, uso de agentes vasopressores e necessidade de terapia de substituição renal durante a internação na Unidade de Terapia Intensiva (UTI), tempo de internação na UTI e tempo de internação hospitalar. Resultados: Foi incluído na análise final o total de 360 pacientes, sendo 180 alocados no grupo albumina e 180 no grupo cristaloide. Em 7 dias, 46 dos 180 pacientes (25,6%) do grupo albumina e 40 dos 180 pacientes do grupo cristaloide (22,2%) morreram (diferença absoluta 3,4%; intervalo de confiança [IC] 95% -5,5 a 12,1%; P=0,458). Em 28 dias, 96 dos 180 pacientes do grupo albumina (53,3%) e 83 dos 180 pacientes do grupo cristaloide (46,1%) morreram (diferença absoluta 7,2%; IC95% -3,1 a 17,3%; P=0,171). Não houve diferença nos desfechos secundários entre os grupos. Conclusões: a utilização da solução de albumina com cristaloide comparada com a solução de cristaloide pura, durante a fase aguda de ressuscitação volêmica da sepse em pacientes com câncer não melhorou a taxa de sobrevida em 7 ou 28 dias. ClinicalTrials: NCT01337934Background: In the last years, the use of albumin to resuscitate septic patients became highly controversial. The aim of his study was to investigate the effects of the administration of albumin and crystalloids, as compared with crystalloids alone, in a population of cancer patients with sepsis. Methods: We performed a single center, randomized, double-blind, controlled-parallel trial between October 2014 and December 2016 at the Cancer Institute of the University of Sao Paulo, Brazil. Cancer patients with severe sepsis or septic shock were randomly assigned to receive either bolus of 500 mL of 4% albumin on crystalloid solution or crystalloid solution alone during the first 6 hours of fluid resuscitation. Primary outcome was defined as death from any cause at 7 days. Secondary outcomes were death from any cause at 28 days, the Sequence Organ Failure Assessment (SOFA) in 7 days, requirements of invasive mechanical ventilation, vasopressor therapy and renal replacement therapy during ICU stay, and length of stay in the ICU and in the hospital. Results: A total of 360 patients were included. At 7 days, 46 of 180 patients (25.6%) in the albumin group and 40 of 180 patients (22.2%) in the crystalloid group had died (absolute difference 3.4%; 95% confidence interval [CI], -5.5 to 12.1%; P=0.458). At 28 days, 96 of 180 patients (53.3%) in the albumin group and 83 of 180 patients (46.1%) in the crystalloid group had died (absolute difference 7.2%; 95%CI -3.1 to 17.3%; P=0.171). No significant differences in other secondary outcomes were observed between groups. Conclusions: The use of albumin replacement in addition to crystalloids, as compared with crystalloids alone, during the early phase of fluid resuscitation of cancer patients with sepsis did not improve the rate of survival at 7 and 28 days. Trial Registration: NCT0133793

Numer. Math. (1999) 81: 539–560

Analysis and computation of a mean-field model for superconductivit

Generalized Newtonian Fluid Flow through a Porous Medium

We present a model for generalized Newtonian fluid flow through a porous medium. In the model the dependence of the fluid viscosity on the velocity is replaced by a dependence on a smoothed (locally averaged) velocity. With appropriate assumptions on the smoothed velocity, existence of a solution to the model is shown. Two examples of smoothing operators are presented in the appendix. A numerical approximation scheme is presented and an a priori error estimate derived. A numerical example is given illustrating the approximation scheme and the a priori error estimate