A low-cost 3D reconstruction system using a single-shot projection of a pattern matrix

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

Development of a methodology for cost determination of wastewater treatment based on functional diagram

This work describes a methodology developed for determination of costs associated to products generated in a small wastewater treatment station for sanitary wastewater from a university campus. This methodology begins with plant component units identification, relating their fluid and thermodynamics features for each point marked in its process diagram. Following, its functional diagram is developed and its formulation is elaborated, in exergetic base, describing all equations for these points, which are the constraints for exergetic production cost problem and are used in equations to determine the costs associated to products generated in SWTS. This methodology was applied to a hypothetical system based on SWTS former parts and presented consistent results when compared to expected values based on previous exergetic expertise. (C) 2008 Elsevier Ltd. All rights reserved.

Development of equations to estimate microbial contamination in ruminal incubation residues of forage produced under tropical conditions using 15N as a label1

The objective of this study was to use 15N to label microbial cells to allow development of equations for estimating the microbial contamination in ruminal in situ incubation residues of forage produced under tropical conditions. A total of 24 tropical forages were ruminal incubated in 3 steers at 3 separate times. To determine microbial contamination of the incubated residues, ruminal bacteria were labeled with 15N by continuous intraruminal infusion 60 h before the first incubation and continued until the last day of incubation. Ruminal digesta was collected for the isolation of bacteria before the first infusion of 15N on adaptation period and after the infusion of 15N on collection period. To determine the microbial contamination of CP fractions, restricted models were compared with the full model using the model identity test. A value of the corrected fraction A was estimated from the corresponding noncorrected fraction by this equation: Corrected A fraction (ACPC) = 1.99286 + 0.98256 × A fraction without correction (ACPWC). The corrected fraction B was estimated from the corresponding noncorrected fraction and from CP, NDF, neutral detergent insoluble protein (NDIP), and indigestible NDF (iNDF) using the equation corrected B fraction (BCPC) = -17.2181 - 0.0344 × fraction B without correction (BCPWC) + 0.65433 × CP + 1.03787 × NDF + 2.66010 × NDIP - 0.85979 × iNDF. The corrected degradation rate of B fraction (kd)was estimated using the equation corrected degradation rate of B fraction (kdCPC) = 0.04667 + 0.35139 × degradation rate of B fraction without correction (kdCPWC) + 0.0020 × CP - 0.00055839 × NDF - 0.00336 × NDIP + 0.00075089 × iNDF. This equation was obtained to estimate the contamination using CP of the feeds: %C = 79.21 × (1 - e-0.0555t) × e-0.0874CP. It was concluded that A and B fractions and kd of CP could be highly biased by microbial CP contamination, and therefore these corrected values could be obtained mathematically, replacing the use of microbial markers. The percentage of contamination and the corrected apparent degradability of CP could be obtained from values of CP and time of incubation for each feed, which could reduce cost and labor involved when using 15N. © 2013 American Society of Animal Science. All rights reserved.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

The determinants of improvements in health outcomes and of cost reduction in hospital inpatient care

This study aims to address two research questions. First, ‘Can we identify factors that are determinants both of improved health outcomes and of reduced costs for hospitalized patients with one of six common diagnoses?’ Second, ‘Can we identify other factors that are determinants of improved health outcomes for such hospitalized patients but which are not associated with costs?’ The Healthcare Cost and Utilization Project (HCUP) Nationwide Inpatient Sample (NIS) database from 2003 to 2006 was employed in this study. The total study sample consisted of hospitals which had at least 30 patients each year for the given diagnosis: 954 hospitals for acute myocardial infarction (AMI), 1552 hospitals for congestive heart failure (CHF), 1120 hospitals for stroke (STR), 1283 hospitals for gastrointestinal hemorrhage (GIH), 979 hospitals for hip fracture (HIP), and 1716 hospitals for pneumonia (PNE). This study used simultaneous equations models to investigate the determinants of improvement in health outcomes and of cost reduction in hospital inpatient care for these six common diagnoses. In addition, the study used instrumental variables and two-stage least squares random effect model for unbalanced panel data estimation. The study concluded that a few factors were determinants of high quality and low cost. Specifically, high specialty was the determinant of high quality and low costs for CHF patients; small hospital size was the determinant of high quality and low costs for AMI patients. Furthermore, CHF patients who were treated in Midwest, South, and West region hospitals had better health outcomes and lower hospital costs than patients who were treated in Northeast region hospitals. Gastrointestinal hemorrhage and pneumonia patients who were treated in South region hospitals also had better health outcomes and lower hospital costs than patients who were treated in Northeast region hospitals. This study found that six non-cost factors were related to health outcomes for a few diagnoses: hospital volume, percentage emergency room admissions for a given diagnosis, hospital competition, specialty, bed size, and hospital region.^

Efficient adaptive methods based on adjoint equations and truncation error estimation for unstructured grids

El propósito de esta tesis es la implementación de métodos eficientes de adaptación de mallas basados en ecuaciones adjuntas en el marco de discretizaciones de volúmenes finitos para mallas no estructuradas. La metodología basada en ecuaciones adjuntas optimiza la malla refinándola adecuadamente con el objetivo de mejorar la precisión de cálculo de un funcional de salida dado. El funcional suele ser una magnitud escalar de interés ingenieril obtenida por post-proceso de la solución, como por ejemplo, la resistencia o la sustentación aerodinámica. Usualmente, el método de adaptación adjunta está basado en una estimación a posteriori del error del funcional de salida mediante un promediado del residuo numérico con las variables adjuntas, “Dual Weighted Residual method” (DWR). Estas variables se obtienen de la solución del problema adjunto para el funcional seleccionado. El procedimiento habitual para introducir este método en códigos basados en discretizaciones de volúmenes finitos involucra la utilización de una malla auxiliar embebida obtenida por refinamiento uniforme de la malla inicial. El uso de esta malla implica un aumento significativo de los recursos computacionales (por ejemplo, en casos 3D el aumento de memoria requerida respecto a la que necesita el problema fluido inicial puede llegar a ser de un orden de magnitud). En esta tesis se propone un método alternativo basado en reformular la estimación del error del funcional en una malla auxiliar más basta y utilizar una técnica de estimación del error de truncación, denominada _ -estimation, para estimar los residuos que intervienen en el método DWR. Utilizando esta estimación del error se diseña un algoritmo de adaptación de mallas que conserva los ingredientes básicos de la adaptación adjunta estándar pero con un coste computacional asociado sensiblemente menor. La metodología de adaptación adjunta estándar y la propuesta en la tesis han sido introducidas en un código de volúmenes finitos utilizado habitualmente en la industria aeronáutica Europea. Se ha investigado la influencia de distintos parámetros numéricos que intervienen en el algoritmo. Finalmente, el método propuesto se compara con otras metodologías de adaptación de mallas y su eficiencia computacional se demuestra en una serie de casos representativos de interés aeronáutico. ABSTRACT The purpose of this thesis is the implementation of efficient grid adaptation methods based on the adjoint equations within the framework of finite volume methods (FVM) for unstructured grid solvers. The adjoint-based methodology aims at adapting grids to improve the accuracy of a functional output of interest, as for example, the aerodynamic drag or lift. The adjoint methodology is based on the a posteriori functional error estimation using the adjoint/dual-weighted residual method (DWR). In this method the error in a functional output can be directly related to local residual errors of the primal solution through the adjoint variables. These variables are obtained by solving the corresponding adjoint problem for the chosen functional. The common approach to introduce the DWR method within the FVM framework involves the use of an auxiliary embedded grid. The storage of this mesh demands high computational resources, i.e. over one order of magnitude increase in memory relative to the initial problem for 3D cases. In this thesis, an alternative methodology for adapting the grid is proposed. Specifically, the DWR approach for error estimation is re-formulated on a coarser mesh level using the _ -estimation method to approximate the truncation error. Then, an output-based adaptive algorithm is designed in such way that the basic ingredients of the standard adjoint method are retained but the computational cost is significantly reduced. The standard and the new proposed adjoint-based adaptive methodologies have been incorporated into a flow solver commonly used in the EU aeronautical industry. The influence of different numerical settings has been investigated. The proposed method has been compared against different grid adaptation approaches and the computational efficiency of the new method has been demonstrated on some representative aeronautical test cases.

Towards cost reduction in concentrating solar power: innovative design for an efficient fresnel based solar field

Energía termosolar (de concentración) es uno de los nombres que hacen referencia en español al término inglés “concentrating solar power”. Se trata de una tecnología basada en la captura de la potencia térmica de la radiación solar, de forma que permita alcanzar temperaturas capaces de alimentar un ciclo termodinámico convencional (o avanzado); el futuro de esta tecnología depende principalmente de su capacidad para concentrar la radiación solar de manera eficiente y económica. La presente tesis está orientada hacia la resolución de ciertos problemas importantes relacionados con este objetivo. La mencionada necesidad de reducir costes en la concentración de radiación solar directa, asegurando el objetivo termodinámico de calentar un fluido hasta una determinada temperatura, es de vital importancia. Los colectores lineales Fresnel han sido identificados en la literatura científica como una tecnología con gran potencial para alcanzar esta reducción de costes. Dicha tecnología ha sido seleccionada por numerosas razones, entre las que destacan su gran libertad de diseño y su actual estado inmaduro. Con el objetivo de responder a este desafío se desarrollado un detallado estudio de las propiedades ópticas de los colectores lineales Fresnel, para lo cual se han utilizado métodos analíticos y numéricos de manera combinada. En primer lugar, se han usado unos modelos para la predicción de la localización y la irradiación normal directa del sol junto a unas relaciones analíticas desarrolladas para estudiar el efecto de múltiples variables de diseño en la energía incidente sobre los espejos. Del mismo modo, se han obtenido analíticamente los errores debidos al llamado “off-axis aberration”, a la apertura de los rayos reflejados en los espejos y a las sombras y bloqueos entre espejos. Esto ha permitido la comparación de diferentes formas de espejo –planos, circulares o parabólicos–, así como el diseño preliminar de la localización y anchura de los espejos y receptor sin necesidad de costosos métodos numéricos. En segundo lugar, se ha desarrollado un modelo de trazado de rayos de Monte Carlo con el objetivo de comprobar la validez del estudio analítico, pero sobre todo porque este no es preciso en el estudio de la reflexión en espejos. El código desarrollado está específicamente ideado para colectores lineales Fresnel, lo que ha permitido la reducción del tiempo de cálculo en varios órdenes de magnitud en comparación con un programa comercial más general. Esto justifica el desarrollo de un nuevo código en lugar de la compra de una licencia de otro programa. El modelo ha sido usado primeramente para comparar la intensidad de flujo térmico y rendimiento de colectores Fresnel, con y sin reflector secundario, con los colectores cilíndrico parabólicos. Finalmente, la conjunción de los resultados obtenidos en el estudio analítico con el programa numérico ha sido usada para optimizar el campo solar para diferentes orientaciones –Norte-Sur y Este-Oeste–, diferentes localizaciones –Almería y Aswan–, diferentes inclinaciones hacia el Trópico –desde 0 deg hasta 32 deg– y diferentes mínimos de intensidad del flujo en el centro del receptor –10 kW/m2 y 25 kW/m2–. La presente tesis ha conducido a importantes descubrimientos que deben ser considerados a la hora de diseñar un campo solar Fresnel. En primer lugar, los espejos utilizados no deben ser plano, sino cilíndricos o parabólicos, ya que los espejos curvos implican mayores concentraciones y rendimiento. Por otro lado, se ha llegado a la conclusión de que la orientación Este-Oeste es más propicia para localizaciones con altas latitudes, como Almería, mientras que en zonas más cercanas a los trópicos como Aswan los campos Norte-Sur conducen a mayores rendimientos. Es de destacar que la orientación Este-Oeste requiere aproximadamente la mitad de espejos que los campos Norte-Sur, puediendo estar inclinados hacia los Trópicos para mejorar el rendimiento, y que alcanzan parecidos valores de intensidad térmica en el receptor todos los días a mediodía. Sin embargo, los campos con orientación Norte-Sur permiten un flujo más constante a lo largo de un día. Por último, ha sido demostrado que el uso de diseños pre-optimizados analíticamente, con anchura de espejos y espaciado entre espejos variables a lo ancho del campo, pueden implicar aumentos de la energía generada por metro cuadrado de espejos de hasta el 6%. El rendimiento óptico anual de los colectores cilíndrico parabólicos es 23 % mayor que el rendimiento de los campos Fresnel en Almería, mientras que la diferencia es de solo 9 % en Aswan. Ello implica que, para alcanzar el mismo precio de electricidad que la tecnología de referencia, la reducción de costes de instalación por metro cuadrado de espejo debe estar entre el 10 % y el 25 %, y que los colectores lineales Fresnel tienen más posibilidades de ser desarrollados en zonas de bajas latitudes. Como consecuencia de los estudios desarrollados en esta tesis se ha patentado un sistema de almacenamiento que tiene en cuenta la variación del flujo térmico en el receptor a lo largo del día, especialmente para campos con orientación Este-Oeste. Este invento permitiría el aprovechamiento de la energía incidente durante más parte del año, aumentando de manera apreciable los rendimientos óptico y térmico. Abstract Concentrating solar power is the common name of a technology based on capturing the thermal power of solar radiation, in a suitable way to reach temperatures able to activate a conventional (or advanced) thermodynamic cycle to generate electricity; this quest mainly depends on our ability to concentrate solar radiation in a cheap and efficient way. The present thesis is focused to highlight and help solving some of the important issues related to this problem. The need of reducing costs in concentrating the direct solar radiation, but without jeopardizing the thermodynamic objective of heating a fluid up to the required temperature, is of prime importance. Linear Fresnel collectors have been identified in the scientific literature as a technology with high potential to reach this cost reduction. This technology has been selected because of a number of reasons, particularly the degrees of freedom of this type of concentrating configuration and its current immature state. In order to respond to this challenge, a very detailed exercise has been carried out on the optical properties of linear Fresnel collectors. This has been done combining analytic and numerical methods. First, the effect of the design variables on the ratio of energy impinging onto the reflecting surface has been studied using analytically developed equations, together with models that predict the location and direct normal irradiance of the sun at any moment. Similarly, errors due to off-axis aberration, to the aperture of the reflected energy beam and to shading and blocking effects have been obtained analytically. This has allowed the comparison of different shapes of mirrors –flat, cylindrical or parabolic–, as well as a preliminary optimization of the location and width of mirrors and receiver with no need of time-consuming numerical models. Second, in order to prove the validity of the analytic results, but also due to the fact that the study of the reflection process is not precise enough when using analytic equations, a Monte Carlo Ray Trace model has been developed. The developed code is designed specifically for linear Fresnel collectors, which has reduced the computing time by several orders of magnitude compared to a wider commercial software. This justifies the development of the new code. The model has been first used to compare radiation flux intensities and efficiencies of linear Fresnel collectors, both multitube receiver and secondary reflector receiver technologies, with parabolic trough collectors. Finally, the results obtained in the analytic study together with the numeric model have used in order to optimize the solar field for different orientations –North-South and East-West–, different locations –Almería and Aswan–, different tilts of the field towards the Tropic –from 0 deg to 32 deg– and different flux intensity minimum requirements –10 kW/m2 and 25 kW/m2. This thesis work has led to several important findings that should be considered in the design of Fresnel solar fields. First, flat mirrors should not be used in any case, as cylindrical and parabolic mirrors lead to higher flux intensities and efficiencies. Second, it has been concluded that, in locations relatively far from the Tropics such as Almería, East-West embodiments are more efficient, while in Aswan North- South orientation leads to a higher annual efficiency. It must be noted that East-West oriented solar fields require approximately half the number of mirrors than NS oriented fields, can be tilted towards the Equator in order to increase the efficiency and attain similar values of flux intensity at the receiver every day at midday. On the other hand, in NS embodiments the flux intensity is more even during each single day. Finally, it has been proved that the use of analytic designs with variable shift between mirrors and variable width of mirrors across the field can lead to improvements in the electricity generated per reflecting surface square meter up to 6%. The annual optical efficiency of parabolic troughs has been found to be 23% higher than the efficiency of Fresnel fields in Almería, but it is only around 9% higher in Aswan. This implies that, in order to attain the same levelized cost of electricity than parabolic troughs, the required reduction of installation costs per mirror square meter is in the range of 10-25%. Also, it is concluded that linear Fresnel collectors are more suitable for low latitude areas. As a consequence of the studies carried out in this thesis, an innovative storage system has been patented. This system takes into account the variation of the flux intensity along the day, especially for East-West oriented solar fields. As a result, the invention would allow to exploit the impinging radiation along longer time every day, increasing appreciably the optical and thermal efficiencies.

The choice of the model in inventory control and the cost of sophistication

This thesis is concerned with the inventory control of items that can be considered independent of one another. The decisions when to order and in what quantity, are the controllable or independent variables in cost expressions which are minimised. The four systems considered are referred to as (Q, R), (nQ,R,T), (M,T) and (M,R,T). Wiith ((Q,R) a fixed quantity Q is ordered each time the order cover (i.e. stock in hand plus on order ) equals or falls below R, the re-order level. With the other three systems reviews are made only at intervals of T. With (nQ,R,T) an order for nQ is placed if on review the inventory cover is less than or equal to R, where n, which is an integer, is chosen at the time so that the new order cover just exceeds R. In (M, T) each order increases the order cover to M. Fnally in (M, R, T) when on review, order cover does not exceed R, enough is ordered to increase it to M. The (Q, R) system is examined at several levels of complexity, so that the theoretical savings in inventory costs obtained with more exact models could be compared with the increases in computational costs. Since the exact model was preferable for the (Q,R) system only exact models were derived for theoretical systems for the other three. Several methods of optimization were tried, but most were found inappropriate for the exact models because of non-convergence. However one method did work for each of the exact models. Demand is considered continuous, and with one exception, the distribution assumed is the normal distribution truncated so that demand is never less than zero. Shortages are assumed to result in backorders, not lost sales. However, the shortage cost is a function of three items, one of which, the backorder cost, may be either a linear, quadratic or an exponential function of the length of time of a backorder, with or without period of grace. Lead times are assumed constant or gamma distributed. Lastly, the actual supply quantity is allowed to be distributed. All the sets of equations were programmed for a KDF 9 computer and the computed performances of the four inventory control procedures are compared under each assurnption.

Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMNb0, with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2394–2402, 2015

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.