4,346 research outputs found
3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries
Recent advances in electron microscopy have enabled the imaging of single
cells in 3D at nanometer length scale resolutions. An uncharted frontier for in
silico biology is the ability to simulate cellular processes using these
observed geometries. Enabling such simulations requires watertight meshing of
electron micrograph images into 3D volume meshes, which can then form the basis
of computer simulations of such processes using numerical techniques such as
the Finite Element Method. In this paper, we describe the use of our recently
rewritten mesh processing software, GAMer 2, to bridge the gap between poorly
conditioned meshes generated from segmented micrographs and boundary marked
tetrahedral meshes which are compatible with simulation. We demonstrate the
application of a workflow using GAMer 2 to a series of electron micrographs of
neuronal dendrite morphology explored at three different length scales and show
that the resulting meshes are suitable for finite element simulations. This
work is an important step towards making physical simulations of biological
processes in realistic geometries routine. Innovations in algorithms to
reconstruct and simulate cellular length scale phenomena based on emerging
structural data will enable realistic physical models and advance discovery at
the interface of geometry and cellular processes. We posit that a new frontier
at the intersection of computational technologies and single cell biology is
now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies
available upon reques
Geodynamo and mantle convection simulations on the Earth Simulator using the Yin-Yang grid
We have developed finite difference codes based on the Yin-Yang grid for the
geodynamo simulation and the mantle convection simulation. The Yin-Yang grid is
a kind of spherical overset grid that is composed of two identical component
grids. The intrinsic simplicity of the mesh configuration of the Yin-Yang grid
enables us to develop highly optimized simulation codes on massively parallel
supercomputers. The Yin-Yang geodynamo code has achieved 15.2 Tflops with 4096
processors on the Earth Simulator. This represents 46% of the theoretical peak
performance. The Yin-Yang mantle code has enabled us to carry out mantle
convection simulations in realistic regimes with a Rayleigh number of
including strongly temperature-dependent viscosity with spatial contrast up to
.Comment: Plenary talk at SciDAC 200
A robust algorithm for implicit description of immersed geometries within a background mesh
The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based on a level-set approach. This distance function allows to consider both, “double-sided” geometries like membrane or shell structures, and “single-sided” objects for which an enclosed volume is univocally defined. For the second case, the discontinuous distance function is complemented by a continuous signed distance function, whereas ray casting is applied to identify the closed volume regions. Furthermore, adaptive mesh refinement is employed to provide the necessary resolution of the background mesh. The proposed algorithm can handle arbitrarily complicated geometries, possibly containing modeling errors (i.e., gaps, overlaps or a non-unique orientation of surface normals). Another important advantage of the algorithm is the embarrassingly parallel nature of its operations. This characteristic allows for a straightforward parallelization using MPI. All developments were implemented within the open source framework “KratosMultiphysics” and are available under the BSD license. The capabilities of the implementation are demonstrated with various application examples involving practice-oriented geometries. The results finally show, that the algorithm is able to describe most complicated geometries within a background mesh, whereas the approximation quality may be directly controlled by mesh refinement.Peer ReviewedPostprint (published version
A tetrahedral space-filling curve for non-conforming adaptive meshes
We introduce a space-filling curve for triangular and tetrahedral
red-refinement that can be computed using bitwise interleaving operations
similar to the well-known Z-order or Morton curve for cubical meshes. To store
sufficient information for random access, we define a low-memory encoding using
10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that
compute the parent, children, and face-neighbors of a mesh element in constant
time, as well as the next and previous element in the space-filling curve and
whether a given element is on the boundary of the root simplex or not. Our
presentation concludes with a scalability demonstration that creates and adapts
selected meshes on a large distributed-memory system.Comment: 33 pages, 12 figures, 8 table
Multi-angle valve seat machining: experimental analysis and numerical modelling
Modern automotive manufacturers operate in highly competitive markets, heavily influenced by Government regulation and ever more environmentally conscious consumers. Modern high-temperature, high-pressure engines that use high hardness multi-angle valve seats are an attractive environmental option, but one that manufacturers find requires more advanced materials and tighter geometric tolerances to maintain engine performance.Tool manufacturers meet these increasingly tougher demands by using, higher hardness cutting materials such as polycrystalline cubic boron nitride (pcBN), that on paper, promise to wear at a lower rate, require less coolant and deliver tighter tolerances than their carbide counterparts.The low brittle fracture toughness of pcBN makes tools that use it vulnerable to minute chipping. A review of literature for this work pointed to no clear answer to this problem, although suggestions range from manufacturing defects, dynamic and flexibility problems with the production line machinery and fixtures, and radial imbalances in the cutting loads.This work set about experimentally investigating those potential explanations, coming to the conclusion that the high radial imbalance of the cutting loads is responsible for pcBN cutting insert failure during multi-angle valve seat machining, and that by simply relocating the cutting inserts around the multi angle cutting tool, the imbalance can be reduced, thus extending the life of the cutting inserts.It is not always easy to predict the imbalance due to the multiple flexibilities in the system, and simulating such a system in 3D with all its associated cutting phenomena such as friction, thermal expansion, chip flow and shearing, would call upon extraordinary computational power and extremely precise experimental inputs to reduce cumulative error.This thesis proves that such a 3D simulation can be made, that runs in exceptionally short durations compared to traditional methods, by making a number of simplifications.MSC Marc was used to host the simulation, with a parametric script written in Python responsible for generating the model geometry and cutter layout. A Fortran program was developed that is called upon by Marc to calculate the required cutting load outputs and generate new workpiece meshes as material is removed.</div
Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures
The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly
transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit
parametrization of boundary surfaces to impose traction and displacement boundary conditions, which
constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing
traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model
generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as
initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer
all boundary terms in the variational formulation into volumetric terms. We show that in the context of the
voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions
defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field,
the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method
by analyzing stresses in a human femur and a vertebral body
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