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7.4 General Similarities

Templated meshes for objects with general similarities are generated using the same setup as described in Section 7.3. Two objects with similarities, one from the field of structural mechanics and one from the field of microelectronics, are investigated in this section:

(i)
A 2D bridge beam construction (Figure 7.10a)
(ii)
A 3D structure with multiple open TSVs [27] (Figure 7.10c)

Figure 7.10: Benchmark objects with similarities

The geometries of the beam bridge construction and the multiple open TSV structure are visualized in top left and bottom left, respectively. The pictures on the right show the templates for the bridge and the multiple open TSV structure. The bridge beam construction has two different templates being the beam and the beam connector. The templated structure consists of $ 31$ beam instances and $ 17$ beam connector instances. The multiple open TSV structure has two templates, being the trunk (bottom right image) and the slice template used in Section 7.3

The expected memory savings and runtime speedups for both objects are not trivial to calculate due to their heterogeneous templated structures. However, the expected memory savings for uniform cell sizes are estimated using the ratio of the sum of the template volumes and the structure instance volume. Memory savings of $ 28.5$ are estimated for the bridge beam construction. The expected memory savings for the multiple open TSV structure are estimated to be a much lower value of $ 1.6$. This low estimation originates from the trunk template. It is only instanced once in the structure instance and has a relative large volume (compared to the volume of the TSVs).

Benchmark results for the bridge beam construction are given in Figure 7.11. Similar to the previous chapters, expected runtime speedups and memory savings are observed for cell counts larger than $ 10^6$. Runtime speedups range from $ 10$ to $ 14$ for meshes with more than $ 10^5$ cells and even exceed $ 28$ for meshes with more than $ 10^6$ cells.
Memory savings, when using the templated mesh data structure without SVB, are larger than $ 25$ for meshes with more than $ 4 \times 10^4$ cells. When using the templated mesh data structure with SVB, the same memory savings are observed for meshes with more than $ 4 \times 10^5$ cells. These benchmark results coincide with the (estimated) expected memory savings.

Figure 7.11: Benchmark results for the 2D bridge beam construction

\begin{subfigure} % latex2html id marker 16257 [b]{0.48\textwidth} \centering ... ...dth]{figures/benchmark/bridge_time} \caption{Runtime speedups} \end{subfigure}

\begin{subfigure} % latex2html id marker 16263 [b]{0.48\textwidth} \centering ... ...width]{figures/benchmark/bridge_size} \caption{Memory savings} \end{subfigure}

Runtime and memory benchmark results are visualized for different cell count values on the left and on the right, respectively. The expected runtime speedups and memory savings are observed for high cell counts (larger than $ 10^6$).

Benchmark results for the multiple 3D open TSV structure are given in Figure 7.12. Runtime speedups range from $ 1.2$ to $ 3.2$, memory savings range from one to $ 1.5$ when using the data structure with SVB and from $ 1.6$ to $ 2.6$ when using the data structure without SVB. However, in contrast to the 2D bridge beam construction, no correlation of the mesh cell count and the memory savings is observed. These benchmark results also coincide well with the (estimated) expected memory savings.

Figure 7.12: Benchmark results for the multiple open TSV structure

\begin{subfigure} % latex2html id marker 16277 [b]{0.48\textwidth} \centering ... ...]{figures/benchmark/multi_tsv_time} \caption{Runtime speedups} \end{subfigure}

\begin{subfigure} % latex2html id marker 16283 [b]{0.48\textwidth} \centering ... ...th]{figures/benchmark/multi_tsv_size} \caption{Memory savings} \end{subfigure}

Runtime and memory benchmarks results are visualized for different cell count values on the left and on the right, respectively. No correlation of the mesh cell count and the memory savings is observed.

next up previous contents
Next: 7.5 FEM-based Symmetry Analysis using a Five-pointed Star Up: 7 Results and Applications Previous: 7.3 Rotational Symmetries   Contents
florian 2016-11-21