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A mechanical model and numerical method for structural membranes implied by all isosurfaces of a level-set function in a three-dimensional bulk domain are proposed. The mechanical model covers large displacements in the context of the…
A higher-order fictitious domain method (FDM) for Reissner-Mindlin shells is proposed which uses a three-dimensional background mesh for the discretization. The midsurface of the shell is immersed into the higher-order background mesh and…
A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear…
This work utilizes the Immersed Boundary Conformal Method (IBCM) to analyze Kirchhoff-Love and Reissner-Mindlin shell structures within an immersed domain framework. Immersed boundary methods involve embedding complex geometries within a…
In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
For the finite element simulation of thin soft biological tissues in dynamics, shell elements, compared to volume elements, can capture the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The…
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…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
The port-Hamiltonian formulation is a powerful method for modeling and interconnecting systems of different natures. In this paper, the port-Hamiltonian formulation in tensorial form of a thick plate described by the Mindlin-Reissner model…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
We present a numerical scheme for the solution of nonlinear mixed-dimensional PDEs describing coupled processes in embedded tubular network system in exchange with a bulk domain. Such problems arise in various biological and technical…