Scan-based immersed isogeometric analysis

Scan-based simulations contain innate topologically complex three-dimensional geometries, represented by large data sets in formats which are not directly suitable for analysis. Consequently, performing high-fidelity scan-based simulations at practical computational costs is still very challenging. The main objective of this dissertation is to develop an efficient and robust scan-based simulation strategy by acquiring a profound understanding of three prominent challenges in scan-based IGA, viz.: i) balancing the accuracy and computational effort associated with numerical integration; ii) the preservation of topology in the spline-based segmentation procedure; and iii) the control of accuracy using error estimation and adaptivity techniques. In three-dimensional immersed isogeometric simulations, the computational effort associated with integration can be the critical component. A myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration, but a general optimal integration framework that suits a broad class of engineering problems is not yet available. In this dissertation we provide a thorough investigation of the accuracy and computational effort of the octree integration technique. We quantify the contribution of the integration error using the theoretical basis provided by Strang’s first lemma. Based on this study we propose an error-estimate-based adaptive integration procedure for immersed IGA. To exploit the advantageous properties of IGA in a scan-based setting, it is important to extract a smooth geometry. This can be established by convoluting the voxel data using B-splines, but this can induce problematic topological changes when features with a size similar to that of the voxels are encountered. This dissertation presents a topology-preserving segmentation procedure using truncated hierarchical (TH)B-splines. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which (TH)B-spline refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. A Fourier analysis is presented to explain the effectiveness of the developed procedure. An additional computational challenge in the context of immersed IGA is the construction of optimal approximations using locally refined splines. For scan-based volumetric domains, hierarchical splines are particularly suitable, as they optimally leverage the advantages offered by the availability of a geometrically simple background mesh. Although truncated hierarchical B-splines have been successfully applied in the context of IGA, their application in the immersed setting is largely unexplored. In this dissertation we propose a computational strategy for the application of error estimation-based mesh adaptivity for stabilized immersed IGA. The conducted analyses and developed computational techniques for scan-based immersed IGA are interrelated, and together constitute a significant improvement in the efficiency and robustness of the analysis paradigm. In combination with other state-of-the-art developments regarding immersed FEM/IGA (\emph{e.g.}, iterative solution techniques, parallel computing), the research in this thesis opens the doors to scan-based simulations with more sophisticated physical behavior, geometries of increased complexity, and larger scan-data sizes.Scan-based simulations contain innate topologically complex three-dimensional geometries, represented by large data sets in formats which are not directly suitable for analysis. Consequently, performing high-fidelity scan-based simulations at practical computational costs is still very challenging. The main objective of this dissertation is to develop an efficient and robust scan-based simulation strategy by acquiring a profound understanding of three prominent challenges in scan-based IGA, viz.: i) balancing the accuracy and computational effort associated with numerical integration; ii) the preservation of topology in the spline-based segmentation procedure; and iii) the control of accuracy using error estimation and adaptivity techniques. In three-dimensional immersed isogeometric simulations, the computational effort associated with integration can be the critical component. A myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration, but a general optimal integration framework that suits a broad class of engineering problems is not yet available. In this dissertation we provide a thorough investigation of the accuracy and computational effort of the octree integration technique. We quantify the contribution of the integration error using the theoretical basis provided by Strang’s first lemma. Based on this study we propose an error-estimate-based adaptive integration procedure for immersed IGA. To exploit the advantageous properties of IGA in a scan-based setting, it is important to extract a smooth geometry. This can be established by convoluting the voxel data using B-splines, but this can induce problematic topological changes when features with a size similar to that of the voxels are encountered. This dissertation presents a topology-preserving segmentation procedure using truncated hierarchical (TH)B-splines. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which (TH)B-spline refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. A Fourier analysis is presented to explain the effectiveness of the developed procedure. An additional computational challenge in the context of immersed IGA is the construction of optimal approximations using locally refined splines. For scan-based volumetric domains, hierarchical splines are particularly suitable, as they optimally leverage the advantages offered by the availability of a geometrically simple background mesh. Although truncated hierarchical B-splines have been successfully applied in the context of IGA, their application in the immersed setting is largely unexplored. In this dissertation we propose a computational strategy for the application of error estimation-based mesh adaptivity for stabilized immersed IGA. The conducted analyses and developed computational techniques for scan-based immersed IGA are interrelated, and together constitute a significant improvement in the efficiency and robustness of the analysis paradigm. In combination with other state-of-the-art developments regarding immersed FEM/IGA (\emph{e.g.}, iterative solution techniques, parallel computing), the research in this thesis opens the doors to scan-based simulations with more sophisticated physical behavior, geometries of increased complexity, and larger scan-data sizes

Modeling and simulation of active fluids

Within cells, the cytoskeleton organizes into polymer networks with unique properties. At short time-scales, they behave elastically. However, due to molecular turnover, at longer time-scales they behave like viscous fluids in low Reynold limit. In addition to this, they are capable of actively developing tension, thanks to molecular motors using chemical energy . At the tissue scale, epithelial cell formed by monolayers can exhibit, in some regimes, a similar active fluid behavior. Contractile forces plays a key role in tissue, for example, in organ development, wound healing, remodeling of the newly synthesized connective tissue, and in sub-cellular level like cell elongation, contraction, rearrangements, cell adhesion, division, cell migration and furrow construction in cytokinesis. Furthermore, as a part of optogenetic technnique, the doped epithelial tissues experience contractility upon illumination. Motivated by this, in the present work we considered a monolayer of cells with illumination as an external power input defined as an tension pattern in space and time to engineer contractility patterns to transport material from one part of the tissue to another or to engineer morphogensis. Altogether, for the system at low Reynold’s limit, governing equations of this compressible active visco-elastic model are developed using traditional continuum approach and Onsager’s variational principle and solved using linear finite elements. The system is non-dimensionalized and the effect of each independent parameter on the system is analyzed. Finally, this model helps in examining the principles that govern the ability to remodel the material by applying space-time patterns of activity

Modeling and simulation of active fluids

Within cells, the cytoskeleton organizes into polymer networks with unique properties. At short time-scales, they behave elastically. However, due to molecular turnover, at longer time-scales they behave like viscous fluids in low Reynold limit. In addition to this, they are capable of actively developing tension, thanks to molecular motors using chemical energy . At the tissue scale, epithelial cell formed by monolayers can exhibit, in some regimes, a similar active fluid behavior. Contractile forces plays a key role in tissue, for example, in organ development, wound healing, remodeling of the newly synthesized connective tissue, and in sub-cellular level like cell elongation, contraction, rearrangements, cell adhesion, division, cell migration and furrow construction in cytokinesis. Furthermore, as a part of optogenetic technnique, the doped epithelial tissues experience contractility upon illumination. Motivated by this, in the present work we considered a monolayer of cells with illumination as an external power input defined as an tension pattern in space and time to engineer contractility patterns to transport material from one part of the tissue to another or to engineer morphogensis. Altogether, for the system at low Reynold’s limit, governing equations of this compressible active visco-elastic model are developed using traditional continuum approach and Onsager’s variational principle and solved using linear finite elements. The system is non-dimensionalized and the effect of each independent parameter on the system is analyzed. Finally, this model helps in examining the principles that govern the ability to remodel the material by applying space-time patterns of activity

Modeling and simulation of active fluids

Within cells, the cytoskeleton organizes into polymer networks with unique properties. At short time-scales, they behave elastically. However, due to molecular turnover, at longer time-scales they behave like viscous fluids in low Reynold limit. In addition to this, they are capable of actively developing tension, thanks to molecular motors using chemical energy . At the tissue scale, epithelial cell formed by monolayers can exhibit, in some regimes, a similar active fluid behavior. Contractile forces plays a key role in tissue, for example, in organ development, wound healing, remodeling of the newly synthesized connective tissue, and in sub-cellular level like cell elongation, contraction, rearrangements, cell adhesion, division, cell migration and furrow construction in cytokinesis. Furthermore, as a part of optogenetic technnique, the doped epithelial tissues experience contractility upon illumination. Motivated by this, in the present work we considered a monolayer of cells with illumination as an external power input defined as an tension pattern in space and time to engineer contractility patterns to transport material from one part of the tissue to another or to engineer morphogensis. Altogether, for the system at low Reynold’s limit, governing equations of this compressible active visco-elastic model are developed using traditional continuum approach and Onsager’s variational principle and solved using linear finite elements. The system is non-dimensionalized and the effect of each independent parameter on the system is analyzed. Finally, this model helps in examining the principles that govern the ability to remodel the material by applying space-time patterns of activity

Error-estimate-based adaptive integration for immersed isogeometric analysis

The Finite Cell Method (FCM) together with Isogeometric analysis (IGA) has been applied successfully in various problems in solid mechanics, in image-based analysis, fluid–structure interaction and in many other applications. A challenging aspect of the isogeometric finite cell method is the integration of cut cells. In particular in three-dimensional simulations the computational effort associated with integration can be the critical component of a simulation. A myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration, but a general optimal integration framework that suits a broad class of engineering problems is not yet available. In this contribution we provide a thorough investigation of the accuracy and computational effort of the octree integration scheme. We quantify the contribution of the integration error using the theoretical basis provided by Strang's first lemma. Based on this study we propose an error-estimate-based adaptive integration procedure for immersed isogeometric analysis. Additionally, we present a detailed numerical investigation of the proposed optimal integration algorithm and its application to immersed isogeometric analysis using two- and three-dimensional linear elasticity problems

Residual-based error estimation and adaptivity for stabilized immersed isogeometric analysis using truncated hierarchical B-splines

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been tailored to the immersed setting by the incorporation of appropriately scaled stabilization and boundary terms. Element-wise error indicators are elaborated for the Laplace and Stokes problems, and a THB-spline-based local mesh refinement strategy is proposed. The error estimation and adaptivity procedure are applied to a series of benchmark problems, demonstrating the suitability of the technique for a range of smooth and non-smooth problems. The adaptivity strategy is also integrated into a scan-based analysis workflow, capable of generating error-controlled results from scan data without the need for extensive user interactions or interventions