| 1. |
- Balaban, Gabriel, et al.
(författare)
-
A Newton Method for Fluid-Structure Interaction Using Full Jacobians Based on Automatic Form Differentiation
- 2012
-
Ingår i: 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012; Vienna; Austria; 10 September 2012 through 14 September 2012. - 9783950353709 ; , s. 3434-3447
-
Konferensbidrag (refereegranskat)abstract
- The study of fluid-structure interaction (FSI) problems is becoming increasingly important both as part of design/engineering and in the modeling of biomedical processes. Examples include the design of new fighter aircraft, the study of the dynamics of heart valves, and the design of prosthetic heart valves. FSI problems are highly coupled and highly nonlinear problems which are challenging to solve. Furthermore, the solution of the discretized system of nonlinear equations is particularly challenging in cases where the solid and the fluid have densities of similar size; this is typically the case for the simulation of biomedical processes involving the deformation of tissue. In such cases, a simple fixed point iteration, in which the solution from a fluid solver is used to impose Neumann boundary conditions for a structure (elasticity), followed by an update of the fluid domain based on the structure solution (via the solution of an auxiliary problem for the update of the fluid mesh), may fail to converge. Instead, a more coupled approach such as a Newton or quasi-Newton method must be employed. In this note, we study the use of Newton's method to solve the fully coupled FSI problem. Typically, a Lagrangian formulation is used to describe the solid; that is, the solid equations are solved on a fixed reference domain (the initial configuration), while an ALE (Arbitrary Lagrangian-Eulerian) formulation is used to describe the fluid. This means that the fluid domain is changing throughout the simulation of a time-dependent problem. The differentiation of the FSI problem, which is required to formulate Newton's method, therefore involves a differentiation with respect to the changing domain of the fluid problem. Such shape differentiation can indeed be used to derive the full Jacobian of the FSI problem; see Fernández and Moubachir [3]. We here study an alternative approach based on mapping the fluid problem back to the initial configuration of the fluid domain. This alternative is advantageous since it allows the use of straightforward differentiation on a fixed domain. This also allows the use of existing tools for automatic differentiation of finite element variational forms such as those developed as part of the FEniCS Project [5-7]. The FEniCS form language UFL [1] is a domain-specific language for finite element variational forms which allows the FSI problem to be expressed in a language close to the mathematical notation. Forms may be differentiated automatically, and automatically assembled into matrices and vectors. The methodology is here applied to the fully nonlinear time-dependent FSI problem modeled by the incompressible Navier-Stokes equations and the St. Venant-Kirchoff nonlinear hyperelastic model.
|
|
| 2. |
- Hoffman, Johan, 1974, et al.
(författare)
-
Mathematics and Computation
- 2004
-
Ingår i: Stockholm Intelligencer: Fourth European Congress of Mathematics.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)
|
|
| 3. |
- Johansson, August, et al.
(författare)
-
A Multimesh Finite Element Method for the Stokes Problem
- 2020
-
Ingår i: Lecture Notes in Computational Science and Engineering. - Cham : Springer International Publishing. - 1439-7358 .- 2197-7100. ; 132, s. 189-198, s. 189-198
-
Konferensbidrag (refereegranskat)abstract
- The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous–discontinuous function space with interface conditions enforced by means of Nitsche’s method. In this contribution, we consider the Stokes problem as a first step towards flow applications. The multimesh formulation leads to so called cut elements in the underlying meshes close to overlaps. These demand stabilization to ensure coercivity and stability of the stiffness matrix. We employ a consistent least-squares term on the overlap to ensure that the inf-sup condition holds. We here present the method for the Stokes problem, discuss the implementation, and verify that we have optimal convergence.
|
|
| 4. |
|
|
| 5. |
|
|
| 6. |
|
|
| 7. |
- Kolibarov, N., et al.
(författare)
-
Roof Segmentation Towards Digital Twin Generation in LoD2+Using Deep Learning
- 2022
-
Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963 .- 2405-8963. ; 55:11, s. 173-178
-
Konferensbidrag (refereegranskat)abstract
- There is an increasing need for digital twins of cities and their base maps, 3D city models. Creating and updating these twins is not an easy task, so automating and streamlining the process is a field of active research. A significant part of the urban geometry is residential buildings and their roofs. Modeling of roofs for urban buildings can be divided into three main areas - building detection, roof recognition and building reconstruction. The building and roofs are segmented with the help of machine learning and image processing. Afterwards the extracted information is used to generate parametric models for the roofs using methods from computational geometry. The goal is to create correct virtual models of roofs belonging to many different types of buildings. In this study, a supervised deep learning approach is proposed for the segmentation of roof edges from a single orthophoto. The predicted features include the linear elements of roofs. The experiments show that, despite the small amount of training data, even in the presence of noise, the proposed method performs well on semantic segmentation of roofs with different shapes and complexities. The quality of the extracted roof elements for the test area is about 56% and 71% for mean intersection over union (IOU) and Dice metric scores, respectively. Copyright (C) 2022 The Authors.
|
|
| 8. |
|
|
| 9. |
- Larsson, Jenny, et al.
(författare)
-
Moving Mesh and Image Registration in FEniCS
- 2017
-
Ingår i: Proceedings of 30th Nordic Seminar on Computational Mechanics – NSCM30. - : Technical University of Denmark. ; , s. 180-183
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Image registration is about finding a transformation that warps a source image into a target image, matching gross features. It is a critical task in medical imaging. Computational anatomy (CA) is a state-of-the-art framework for image registration, founded in the theory of fluid dynamics and PDE: one seeks a time-dependent vector field that generates a continuous warp of the source image into the target image.Here we construct a finite element realisation of CA by representing the continuous warp by a moving mesh. The PDE governing the motion of the mesh is an infinitedimensional nonlinear gradient flow; a brief description is given in section 2. In essence, it is a time-stepping problem, where an elliptic PDE is solved in each time step using the FEniCS finite element package. The solution process is summarised in fig. 1.Although commonly used in medical contexts, we stress that CA has promising applications also in structural engineering, as discussed in section 4.
|
|
| 10. |
- Latino, Fabio, 1990, et al.
(författare)
-
Virtual City@Chalmers: Creating a prototype for a collaborative early stage urban planning AR application
- 2019
-
Ingår i: Proceedings of the 7th Regional International Symposium on Education and Research in Computer Aided Architectural Design in Europe. - 9788772100296 ; , s. 15-24
-
Konferensbidrag (refereegranskat)abstract
- Contemporary urban planning require multi-stakeholder collaboration to create liveable, accessible and resilient cities. Information and communications technologies can play an important role. This paper presents and discusses the development of a prototype for an indoor multi-stakeholder augmented reality (AR) application to support collaborative design in early stage urban planning. The prototype is integrated into VirtualCity@Chalmers, a platform for modeling, simulation, and visualization of urban environments. Based on a user-centered approach, four main steps were carried out: literature study, interview study, development of guidelines, and development of the first version of a collaborative AR prototype. The guidelines for the prototype development address design and layout, collaboration, analysis, and object creation and manipulation. At the current state of development, the AR application allows users to visualize a projection of three-dimensional assets over a flat surface. Further research will focus on user testing and integration of simple Computational Fluid Dynamics simulations.
|
|
