Mesh Insertion of Hybrid Meshes

Our Objectives NHMD The mesh insertion algorithm

Mesh Insertion of Hybrid Meshes M. S. Ebeida*

E. Mestreau**

Y. Zhang*

*Computational Biomodeling Lab, MechE, CMU

S. Dey**

**Naval Research Laboratory

18th International Meshing Roundtable October 27, 2008

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**

Mesh Insertion of Hybrid Meshes


Overview

1

Our Objectives

2

NHMD Overview Query Operations Performance

3

The mesh insertion algorithm Detection of nodes in the overlap region Removal of the undesired entities Connecting the target mesh to the tool mesh

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**



Our Objectives An efficient mesh data structure • Should be able to handle non-manifold hybrid meshes. • Should be optimized for query operations and storage

requirements. An automated tool for mesh insertion • Merging the entities of two mesh models; a tool mesh and a target mesh. • The entities of the tool mesh should be preserved in the final

mesh. • The elements of the target mesh may be modified or

eliminated to avoid the overlapping between the models. • The final mesh should be conforming and crack-free. M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**



Overview Query Operations Performance

A Non-manifold Hybrid Mesh Data structure (NHMD) • The Element-Node Connectivity matrix represent the least

amount of information to be stored for a hybrid mesh. • This matrix can be stored efficiently using the CSR format.

Memory cost = Ne + nnz. • However in order to have an efficient query algorithm, we

need also store the transpose of this mesh with the additional cost of N + nnz. • Since we are dealing with a fixed type of elements (7 types),

we do not need to store the indices of the elements so the storage cost of our data structure is 2 × nnz + N + 7. • We can also avoid storing the nodes indices, reducing the

storage cost to 2 × nnz + 7. However each query operation would require a binary search operation, O (log N ). M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Elements included in NHMD

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




An example problem for NHMD

Stored information Ne = [0 0 0 0 1 1 1]T , CI = [6 7 3 5 7 2 3 2 1] T , CJ = [9 6 8 3 7 4 1 2 5] T , CK = [1 2 4 6 6 7 8]T M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Query Operations in NHMD • The query operations in NHMD are element-node based. • For example if we want to retrieve the neighbor faces of a given edge, we first collect the elements bounded by the nodes of that edge. • Then we get the faces of these elements and return those faces bounded by that edge. • These operations requires a mapping from local indices to global indices, which can done efficiently since we are handling a small set of element types and we store the number of element in each type. • Note that the cost of this query does not depend on the size

of the mesh which implies the optimality of the algorithm. • Some edges and faces might have more that one index but

that does not a problem since we are not storing these indices. • Duplicated entities will have the same bounding nodes, so

they can be detected and removed from the returned list. M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Performance of NHMD using my laptop (2.0 GHz and 2.0 GB RAM) • NHMD is able to handle a

mesh with 10 million nodes. • The mesh and its associated

data structure were generated in 45 seconds. • Recently we have extended

NHMD to include mapping between the mesh entities and associated geometry entities.

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**



Detection of nodes in the overlap region Removal of the undesired entities Connecting the target mesh to the tool mesh

Overview of the algorithm

• Detect the undesired nodes of the target mesh (inside or too

close to the tool mesh). • Remove any element from the target mesh with an undesired

node. • Execute a 2-steps advancing front algorithm to connect the

terminal nodes of the target mesh to the tool mesh. • If the connection region is 3-dimensional, we need to ensure

that the bounding surface are smooth and almost parallel.

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Detection of nodes in the overlap region

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Detection of nodes in the overlap region

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Line (Beam) elements

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Surface elements

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Volumetric elements - Challenging Problem

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Volumetric elements - Generation of Boundary Layer

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Volumetric elements - Surface Extraction

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Volumetric elements - Connection

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Volumetric elements - Connection

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Examples

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Examples

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**




Thank you!

M. S. Ebeida*

E. Mestreau**

Y. Zhang*

S. Dey**
