A coupling technique for non-matching finite element meshes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.

The influence of non-matching implant and abutment diameters on radiographic crestal bone levels in dogs

BACKGROUND: It has been shown that different implant designs and different vertical implant positions have an influence on crestal bone levels. The aim of the present study was to evaluate radiographic crestal bone changes around experimental dental implants with non-matching implant-abutment diameters placed submucosally or transmucosally at three different levels relative to the alveolar crest. METHODS: Sixty two-piece dental implants with non-matching implant-abutment diameters were placed in edentulous spaces bilaterally in five foxhounds. The implants were placed submucosally or transmucosally in the left or the right side of the mandible. Within each side, six implants were randomly placed at three distinct levels relative to the alveolar crest. After 12 weeks, 60 crowns were cemented. Radiographs were obtained from all implant sites following implant placement, after crown insertion, and monthly for 6 months after loading. RESULTS: Radiographic analysis revealed very little bone loss and a slight increase in bone level for implants placed at the level of the crest or 1 mm above. The greatest bone loss occurred at implants placed 1 mm below the bone crest. No clinically significant differences regarding marginal bone loss and the level of the bone-to-implant contact were detected between implants with a submucosal or a transmucosal healing. CONCLUSIONS: Implants with non-matching implant-abutment diameters demonstrated some bone loss; however, it was a small amount. There was no clinically significant difference between submucosal and transmucosal approaches.

Bone response to loaded implants with non-matching implant-abutment diameters in the canine mandible

BACKGROUND: One way to evaluate various implant restorations is to measure the amount of bone change that occurs at the crestal bone. The objective of this study was to histologically evaluate the alveolar bone change around a bone-level, non-matching implant-abutment diameter configuration that incorporated a horizontal offset and a Morse taper internal connection. METHODS: The study design included extraction of all mandibular premolars and first molars in five canines. After 3 months, 12 dental implants were placed at three levels in each dog: even with the alveolar crest, 1 mm above the alveolar crest, and 1 mm below the alveolar crest. The implants were submerged on one side of the mandible. On the other side, healing abutments were exposed to the oral cavity (non-submerged). Gold crowns were attached 2 months after implant placement. The dogs were sacrificed 6 months postloading, and specimens were processed for histologic and histometric analyses. RESULTS: Evaluation of the specimens indicated that the marginal bone remained near the top of the implants under submerged and non-submerged conditions. The amount of bone change for submerged implants placed even with, 1 mm below, and 1 mm above the alveolar crest was -0.34, -1.29, and 0.04 mm, respectively (negative values indicate bone loss). For non-submerged implants, the respective values were -0.38, -1.13, and 0.19 mm. For submerged and non-submerged implants, there were significant differences in the amount of bone change among the three groups (P <0.05). The percentage of bone-to-implant contact for submerged implants was 73.3%, 71.8%, and 71.5%. For non-submerged implants, the respective numbers were 73.2%, 74.5%, and 76%. No significant differences occurred with regard to the percentage of bone contact. CONCLUSIONS: Minimal histologic bone loss occurred when dental implants with non-matching implant-abutment diameters were placed at the bone crest and were loaded for 6 months in the canine. The bone loss was significantly less (five- to six-fold) than that reported for bone-level implants with matching implant-abutment diameters (butt-joint connections).

Um modelo multiescala concorrente para representar o processo de fissuração do concreto.

Este trabalho propõe uma técnica de modelagem multiescala concorrente do concreto considerando duas escalas distintas: a mesoescala, onde o concreto é modelado como um material heterogêneo, e a macroescala, na qual o concreto é tratado como um material homogêneo. A heterogeneidade da estrutura mesoscópica do concreto é idealizada considerando três fases distintas, compostas pelos agregados graúdos e argamassa (matriz), estes considerados materiais homogêneos, e zona de transição interfacial (ZTI), tratada como a parte mais fraca entre as três fases. O agregado graúdo é gerado a partir de uma curva granulométrica e posicionado na matriz de forma aleatória. Seu comportamento mecânico é descrito por um modelo constitutivo elástico-linear, devido a sua maior resistência quando comparado com as outras duas fases do concreto. Elementos finitos contínuos com alta relação de aspecto em conjunto com um modelo constitutivo de dano são usados para representar o comportamento não linear do concreto, decorrente da iniciação de fissuras na ZTI e posterior propagação para a matriz, dando lugar à formação de macrofissuras. Os elementos finitos de interface com alta relação de aspecto são inseridos entre todos os elementos regulares da matriz e entre os da matriz e agregados, representando a ZTI, tornando-se potenciais caminhos de propagação de fissuras. No estado limite, quando a espessura do elemento de interface tende a zero (h ?0) e, consequentemente, a relação de aspecto tende a infinito, estes elementos apresentam a mesma cinemática da aproximação contínua de descontinuidades fortes (ACDF), sendo apropriados para representar a formação de descontinuidades associados a fissuras, similar aos modelos coesivos. Um modelo de dano à tração é proposto para representar o comportamento mecânico não linear das interfaces, associado à formação de fissuras, ou até mesmo ao eventual fechamento destas. A fim de contornar os problemas causados pela malha de elementos finitos de transição entre as malhas da macro e da mesoescala, que, em geral, apresentam diferenças expressivas 5 de refinamento, utiliza-se uma técnica recente de acoplamento de malhas não conformes. Esta técnica é baseada na definição de elementos finitos de acoplamento (EFAs), os quais são capazes de estabelecer a continuidade de deslocamento entre malhas geradas de forma completamente independentes, sem aumentar a quantidade total de graus de liberdade do problema, podendo ser utilizados tanto para acoplar malhas não sobrepostas quanto sobrepostas. Para tornar possível a análise em multiescala em casos nos quais a região de localização de deformações não pode ser definida a priori, propõe-se uma técnica multiescala adaptativa. Nesta abordagem, usa-se a distribuição de tensões da escala macroscópica como um indicador para alterar a modelagem das regiões críticas, substituindo-se a macroescala pela mesoescala durante a análise. Consequentemente, a malha macroscópica é automaticamente substituída por uma malha mesoscópica, onde o comportamento não linear está na iminência de ocorrer. Testes numéricos são desenvolvidos para mostrar a capacidade do modelo proposto de representar o processo de iniciação e propagação de fissuras na região tracionada do concreto. Os resultados numéricos são comparados com os resultados experimentais ou com aqueles obtidos através da simulação direta em mesoescala (SDM).

Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes

This paper is concerned with the discontinuous Galerkin approximation of the Maxwell eigenproblem. After reviewing the theory developed in [5], we present a set of numerical experiments which both validate the theory, and provide further insight regarding the practical performance of discontinuous Galerkin methods, particularly in the case when non-conforming meshes, characterized by the presence of hanging nodes, are employed.

Evidence evaluation in fingerprint comparison and automated fingerprint identification systems: modeling between finger variability

In the context of the investigation of the use of automated fingerprint identification systems (AFIS) for the evaluation of fingerprint evidence, the current study presents investigations into the variability of scores from an AFIS system when fingermarks from a known donor are compared to fingerprints that are not from the same source. The ultimate goal is to propose a model, based on likelihood ratios, which allows the evaluation of mark-to-print comparisons. In particular, this model, through its use of AFIS technology, benefits from the possibility of using a large amount of data, as well as from an already built-in proximity measure, the AFIS score. More precisely, the numerator of the LR is obtained from scores issued from comparisons between impressions from the same source and showing the same minutia configuration. The denominator of the LR is obtained by extracting scores from comparisons of the questioned mark with a database of non-matching sources. This paper focuses solely on the assignment of the denominator of the LR. We refer to it by the generic term of between-finger variability. The issues addressed in this paper in relation to between-finger variability are the required sample size, the influence of the finger number and general pattern, as well as that of the number of minutiae included and their configuration on a given finger. Results show that reliable estimation of between-finger variability is feasible with 10,000 scores. These scores should come from the appropriate finger number/general pattern combination as defined by the mark. Furthermore, strategies of obtaining between-finger variability when these elements cannot be conclusively seen on the mark (and its position with respect to other marks for finger number) have been presented. These results immediately allow case-by-case estimation of the between-finger variability in an operational setting.

Evaluation of two experimental models of hepatic encephalopathy in rats

The serious neuropsychological repercussions of hepatic encephalopathy have led to the creation of several experimental models in order to better understand the pathogenesis of the disease. In the present investigation, two possible causes of hepatic encephalopathy, cholestasis and portal hypertension, were chosen to study the behavioral impairments caused by the disease using an object recognition task. This working memory test is based on a paradigm of spontaneous delayed non-matching to sample and was performed 60 days after surgery. Male Wistar rats (225-250 g) were divided into three groups: two experimental groups, microsurgical cholestasis (N = 20) and extrahepatic portal hypertension (N = 20), and a control group (N = 20). A mild alteration of the recognition memory occurred in rats with cholestasis compared to control rats and portal hypertensive rats. The latter group showed the poorest performance on the basis of the behavioral indexes tested. In particular, only the control group spent significantly more time exploring novel objects compared to familiar ones (P < 0.001). In addition, the portal hypertension group spent the shortest time exploring both the novel and familiar objects (P < 0.001). These results suggest that the existence of portosystemic collateral circulation per se may be responsible for subclinical encephalopathy.

Operant serial feature-positive conditional discrimination with composite features and different topography responses

In a serial feature-positive conditional discrimination procedure the properties of a target stimulus A are defined by the presence or not of a feature stimulus X preceding it. In the present experiment, composite features preceded targets associated with two different topography operant responses (right and left bar pressing); matching and non-matching-to-sample arrangements were also used. Five water-deprived Wistar rats were trained in 6 different trials: X-R®Ar and X-L®Al, in which X and A were same modality visual stimuli and the reinforcement was contingent to pressing either the right (r) or left (l) bar that had the light on during the feature (matching-to-sample); Y-R®Bl and Y-L®Br, in which Y and B were same modality auditory stimuli and the reinforcement was contingent to pressing the bar that had the light off during the feature (non-matching-to-sample); A- and B- alone. After 100 training sessions, the animals were submitted to transfer tests with the targets used plus a new one (auditory click). Average percentages of stimuli with a response were measured. Acquisition occurred completely only for Y-L®Br+; however, complex associations were established along training. Transfer was not complete during the tests since concurrent effects of extinction and response generalization also occurred. Results suggest the use of both simple conditioning and configurational strategies, favoring the most recent theories of conditional discrimination learning. The implications of the use of complex arrangements for discussing these theories are considered.

Imitation of lateralised body movements: doing it the hard way

Two experiments examined imitation of lateralised body movement sequences presented at six viewing angles (0º, 60º, 120º, 180º, 240º, and 300º rotation relative to the participant’s body). Experiment 1 found that, when participants were instructed simply to ‘‘do what the model does’’, at all viewing angles they produced more actions using the same side of the body as the model (anatomical matches), than actions using the opposite side (anatomical non-matches). In Experiment 2 participants were instructed to produce either anatomical matches or anatomical non-matches of observed actions. When the model was viewed from behind (0º), the anatomically matching group were more accurate than the anatomically non-matching group, but the non-matching group was superior when the model faced the participant (180º and 240º). No reliable differences were observed between groups at 60º, 120º, and 300º. In combination, the results of Experiments 1 and 2 suggest that, when they are confronting a model, people choose to imitate the hard way; they attempt to match observed actions anatomically, in spite of the fact that anatomical matching is more subject to error than anatomical non-matching.

Development and validation of a D-loop mtDNA SNP assay for the screening of specimens in forensic casework

Mitochondrial DNA (mtDNA) analysis is usually a last resort in routine forensic DNA casework. However, it has become a powerful tool for the analysis of highly degraded samples or samples containing too little or no nuclear DNA, such as old bones and hair shafts. The gold standard methodology still constitutes the direct sequencing of polymerase chain reaction (PCR) products or cloned amplicons from the HVS-1 and HVS-2 (hypervariable segment) control region segments. Identifications using mtDNA are time consuming, expensive and can be very complex, depending on the amount and nature of the material being tested. The main goal of this work is to develop a less labour-intensive and less expensive screening method for mtDNA analysis, in order to aid in the exclusion of non-matching samples and as a presumptive test prior to final confirmatory DNA sequencing. We have selected 14 highly discriminatory single nucleotide polymorphisms (SNPs) based on simulations performed by Salas and Amigo (2010) [1] to be typed using SNaPShotTM (Applied Biosystems, Foster City, CA, USA). The assay was validated by typing more than 100 HVS-1/HVS-2 sequenced samples. No differences were observed between the SNP typing and DNA sequencing when results were compared, with the exception of allelic dropouts observed in a few haplotypes. Haplotype diversity simulations were performed using 172 mtDNA sequences representative of the Brazilian population and a score of 0.9794 was obtained when the 14 SNPs were used, showing that the theoretical prediction approach for the selection of highly discriminatory SNPs suggested by Salas and Amigo (2010) [1] was confirmed in the population studied. As the main goal of the work is to develop a screening assay to skip the sequencing of all samples in a particular case, a pair-wise comparison of the sequences was done using the selected SNPs. When both HVS-1/HVS-2 SNPs were used for simulations, at least two differences were observed in 93.2% of the comparisons performed. The assay was validated with casework samples. Results show that the method is straightforward and can be used for exclusionary purposes, saving time and laboratory resources. The assay confirms the theoretic prediction suggested by Salas and Amigo (2010) [1]. All forensic advantages, such as high sensitivity and power of discrimination, as also the disadvantages, such as the occurrence of allele dropouts, are discussed throughout the article. © 2013 Elsevier B.V.

P-233-Biodiversity of mucosa associated microbiome of Crohn's disease patients living in middle western São Paulo State, Brazil

Background: The intestinal microbiome (IM) has extensively been studied in the search for a link of bacteria with the cause of Crohn`s disease (CD). The association might result from the action of a specific pathogen and/or an eventual imbalance in bacterial species composition of the gut. The innumerous virulence associated markers and strategies described for adherent and invasive Escherichia coli (AIEC) have made them putative candidate pathogens for CD. IM of CD patients shows dysbiosis, manifested by the proliferation of bacterial groups such as Enterobacteriaceae and reduction of others such as Lactobacillus and Bifidobacterium. The augmented bacterial population comprising of commensal and/or pathogenic organisms super stimulates the immune system, triggering the inflammatory reactions responsible for the clinical manifestations of the disease. Considering the role played by IM in CD and the multiple variables influencing its species composition, resulting in differences among populations, the objective of this study was to determine the bacterial biodiversity in the mucosa associated microbiome of CD patients from a population not previously subject to this analysis, living in the middle west region of Sao Paulo state. Methods: A total of 4 CD patients and 5 controls subjects attending the Botucatu Medical School of the Sao Paulo State University (UNESP) for routine colonoscopy and who signed an informed consent were included in the study. A number of 2 biopsies, one from the ileum and other from any part of the terminal colon, were taken from each subject and immediately frozen at -70[degrees]C until DNA purification. The bacterial biodiversity was assessed by next generation (ion torrent) sequencing of PCR amplicons of the ribosomal DNA 16S V6 region (16S V6 rDNA). The bacterial identification was performed at the genus level, by alignment of the generated DNA sequences with those available at the ribosomal database project (RDP) website. Results: The overall DNA sequence output was based on an average number of 526,427 reads per run, matching 50 bacterial genus 16SrDNA sequences available at the RDB website, and 22 non matching sequences. Over 95% of the sequences corresponded to taxa belonging to the major phyla: Firmicutes, Bacterioidetes, Proteobacteria and Actinobacteria. Irrespective of the intestinal site analyzed, no case-control differences could be observed in the prevalence of Actinobacteria and Firmicutes. The prevalence of Proteobacteria was higher (40%) in the biopsies of control subjects as compared to that of DC patients (16%). For Bacterioidetes, the higher prevalence was observed among DC patients (33% as opposed to 14,5% in controls). The significance for all comparisons considered a p value < 0,05 in a Chi2 test. No mucosal site specific differences could be observed in IM comparisons of CD and control subjects. Conclusions: The rise in the number of Bacterioidetes observed here among CD patients seems to be in agreement with most of studies published thus far. Yet, the reduction in the number of Proteobacteria along with an apparently unaltered population of Actinobacteria and Firmicutes, which include the so called "beneficial" organisms Bifidobacterium and Lactobacillus were rather surprising. These data suggest that the analyses on the role of IM in CD should consider the multiple variables that may influence its species composition.

Porous Polymeric Bioresorbable Scaffolds for Tissue Engineering

Tissue engineering is a discipline that aims at regenerating damaged biological tissues by using a cell-construct engineered in vitro made of cells grown into a porous 3D scaffold. The role of the scaffold is to guide cell growth and differentiation by acting as a bioresorbable temporary substrate that will be eventually replaced by new tissue produced by cells. As a matter or fact, the obtainment of a successful engineered tissue requires a multidisciplinary approach that must integrate the basic principles of biology, engineering and material science. The present Ph.D. thesis aimed at developing and characterizing innovative polymeric bioresorbable scaffolds made of hydrolysable polyesters. The potentialities of both commercial polyesters (i.e. poly-e-caprolactone, polylactide and some lactide copolymers) and of non-commercial polyesters (i.e. poly-w-pentadecalactone and some of its copolymers) were explored and discussed. Two techniques were employed to fabricate scaffolds: supercritical carbon dioxide (scCO2) foaming and electrospinning (ES). The former is a powerful technology that enables to produce 3D microporous foams by avoiding the use of solvents that can be toxic to mammalian cells. The scCO2 process, which is commonly applied to amorphous polymers, was successfully modified to foam a highly crystalline poly(w-pentadecalactone-co-e-caprolactone) copolymer and the effect of process parameters on scaffold morphology and thermo-mechanical properties was investigated. In the course of the present research activity, sub-micrometric fibrous non-woven meshes were produced using ES technology. Electrospun materials are considered highly promising scaffolds because they resemble the 3D organization of native extra cellular matrix. A careful control of process parameters allowed to fabricate defect-free fibres with diameters ranging from hundreds of nanometers to several microns, having either smooth or porous surface. Moreover, versatility of ES technology enabled to produce electrospun scaffolds from different polyesters as well as “composite” non-woven meshes by concomitantly electrospinning different fibres in terms of both fibre morphology and polymer material. The 3D-architecture of the electrospun scaffolds fabricated in this research was controlled in terms of mutual fibre orientation by properly modifying the instrumental apparatus. This aspect is particularly interesting since the micro/nano-architecture of the scaffold is known to affect cell behaviour. Since last generation scaffolds are expected to induce specific cell response, the present research activity also explored the possibility to produce electrospun scaffolds bioactive towards cells. Bio-functionalized substrates were obtained by loading polymer fibres with growth factors (i.e. biomolecules that elicit specific cell behaviour) and it was demonstrated that, despite the high voltages applied during electrospinning, the growth factor retains its biological activity once released from the fibres upon contact with cell culture medium. A second fuctionalization approach aiming, at a final stage, at controlling cell adhesion on electrospun scaffolds, consisted in covering fibre surface with highly hydrophilic polymer brushes of glycerol monomethacrylate synthesized by Atom Transfer Radical Polymerization. Future investigations are going to exploit the hydroxyl groups of the polymer brushes for functionalizing the fibre surface with desired biomolecules. Electrospun scaffolds were employed in cell culture experiments performed in collaboration with biochemical laboratories aimed at evaluating the biocompatibility of new electrospun polymers and at investigating the effect of fibre orientation on cell behaviour. Moreover, at a preliminary stage, electrospun scaffolds were also cultured with tumour mammalian cells for developing in vitro tumour models aimed at better understanding the role of natural ECM on tumour malignity in vivo.

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Esta tesis propone una completa formulación termo-mecánica para la simulación no-lineal de mecanismos flexibles basada en métodos libres de malla. El enfoque se basa en tres pilares principales: la formulación de Lagrangiano total para medios continuos, la discretización de Bubnov-Galerkin, y las funciones de forma libres de malla. Los métodos sin malla se caracterizan por la definición de un conjunto de funciones de forma en dominios solapados, junto con una malla de integración de las ecuaciones discretas de balance. Dos tipos de funciones de forma se han seleccionado como representación de las familias interpolantes (Funciones de Base Radial) y aproximantes (Mínimos Cuadrados Móviles). Su formulación se ha adaptado haciendo sus parámetros compatibles, y su ausencia de conectividad predefinida se ha aprovechado para interconectar múltiples dominios de manera automática, permitiendo el uso de mallas de fondo no conformes. Se propone una formulación generalizada de restricciones, juntas y contactos, válida para sólidos rígidos y flexibles, siendo estos últimos discretizados mediante elementos finitos (MEF) o libres de malla. La mayor ventaja de este enfoque reside en que independiza completamente el dominio con respecto de las uniones y acciones externas a cada sólido, permitiendo su definición incluso fuera del contorno. Al mismo tiempo, también se minimiza el número de ecuaciones de restricción necesarias para la definición de uniones realistas. Las diversas validaciones, ejemplos y comparaciones detalladas muestran como el enfoque propuesto es genérico y extensible a un gran número de sistemas. En concreto, las comparaciones con el MEF indican una importante reducción del error para igual número de nodos, tanto en simulaciones mecánicas, como térmicas y termo-mecánicas acopladas. A igualdad de error, la eficiencia numérica de los métodos libres de malla es mayor que la del MEF cuanto más grosera es la discretización. Finalmente, la formulación se aplica a un problema de diseño real sobre el mantenimiento de estructuras masivas en el interior de un reactor de fusión, demostrando su viabilidad en análisis de problemas reales, y a su vez mostrando su potencial para su uso en simulación en tiempo real de sistemas no-lineales. A new complete formulation is proposed for the simulation of nonlinear dynamic of multibody systems with thermo-mechanical behaviour. The approach is founded in three main pillars: total Lagrangian formulation, Bubnov-Galerkin discretization, and meshfree shape functions. Meshfree methods are characterized by the definition of a set of shape functions in overlapping domains, and a background grid for integration of the Galerkin discrete equations. Two different types of shape functions have been chosen as representatives of interpolation (Radial Basis Functions), and approximation (Moving Least Squares) families. Their formulation has been adapted to use compatible parameters, and their lack of predefined connectivity is used to interconnect different domains seamlessly, allowing the use of non-conforming meshes. A generalized formulation for constraints, joints, and contacts is proposed, which is valid for rigid and flexible solids, being the later discretized using either finite elements (FEM) or meshfree methods. The greatest advantage of this approach is that makes the domain completely independent of the external links and actions, allowing to even define them outside of the boundary. At the same time, the number of constraint equations needed for defining realistic joints is minimized. Validation, examples, and benchmarks are provided for the proposed formulation, demonstrating that the approach is generic and extensible to further problems. Comparisons with FEM show a much lower error for the same number of nodes, both for mechanical and thermal analyses. The numerical efficiency is also better when coarse discretizations are used. A final demonstration to a real problem for handling massive structures inside of a fusion reactor is presented. It demonstrates that the application of meshfree methods is feasible and can provide an advantage towards the definition of nonlinear real-time simulation models.

Método multigrid algébrico: reutilização das estruturas multigrid no transporte de contaminantes

A necessidade de obter solução de grandes sistemas lineares resultantes de processos de discretização de equações diferenciais parciais provenientes da modelagem de diferentes fenômenos físicos conduz à busca de técnicas numéricas escaláveis. Métodos multigrid são classificados como algoritmos escaláveis.Um estimador de erros deve estar associado à solução numérica do problema discreto de modo a propiciar a adequada avaliação da solução obtida pelo processo de aproximação. Nesse contexto, a presente tese caracteriza-se pela proposta de reutilização das estruturas matriciais hierárquicas de operadores de transferência e restrição dos métodos multigrid algébricos para acelerar o tempo de solução dos sistemas lineares associados à equação do transporte de contaminantes em meio poroso saturado. Adicionalmente, caracteriza-se pela implementação das estimativas residuais para os problemas que envolvem dados constantes ou não constantes, os regimes de pequena ou grande advecção e pela proposta de utilização das estimativas residuais associadas ao termo de fonte e à condição inicial para construir procedimentos adaptativos para os dados do problema. O desenvolvimento dos códigos do método de elementos finitos, do estimador residual e dos procedimentos adaptativos foram baseados no projeto FEniCS, utilizando a linguagem de programação PYTHONR e desenvolvidos na plataforma Eclipse. A implementação dos métodos multigrid algébricos com reutilização considera a biblioteca PyAMG. Baseado na reutilização das estruturas hierárquicas, os métodos multigrid com reutilização com parâmetro fixo e automática são propostos, e esses conceitos são estendidos para os métodos iterativos não-estacionários tais como GMRES e BICGSTAB. Os resultados numéricos mostraram que o estimador residual captura o comportamento do erro real da solução numérica, e fornece algoritmos adaptativos para os dados cuja malha retornada produz uma solução numérica similar à uma malha uniforme com mais elementos. Adicionalmente, os métodos com reutilização são mais rápidos que os métodos que não empregam o processo de reutilização de estruturas. Além disso, a eficiência dos métodos com reutilização também pode ser observada na solução do problema auxiliar, o qual é necessário para obtenção das estimativas residuais para o regime de grande advecção. Esses resultados englobam tanto os métodos multigrid algébricos do tipo SA quanto os métodos pré-condicionados por métodos multigrid algébrico SA, e envolvem o transporte de contaminantes em regime de pequena e grande advecção, malhas estruturadas e não estruturadas, problemas bidimensionais, problemas tridimensionais e domínios com diferentes escalas.