Related papers: Fast immersed boundary method based on weighted qu…
Standard finite element methods employ an element-wise assembly strategy. The element's contribution to the system matrix is formed by a loop over quadrature points. This concept is also used in fictitious domain methods, which perform…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…
We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…
Data in the form of images or higher-order tensors is ubiquitous in modern deep learning applications. Owing to their inherent high dimensionality, the need for subquadratic layers processing such data is even more pressing than for…
In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows.…
A projection-based immersed boundary method is dominated by sparse linear algebra routines. Using the open-source Cusp library, we observe a speedup (with respect to a single CPU core) which reflects the constraints of a bandwidth-dominated…
In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already…
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries,…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…
The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with…