biology

Parallel mesh generation

Parallel mesh generation is a biology topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Parallel mesh generation rather than just read about it. In short: Parallel mesh generation in numerical analysis is a new research area between the boundaries of two scientific computing disciplines: computational geometry and parallel computing. Parallel mesh generation methods decompose the original mesh generation problem into smaller subproblems which are solved (meshed) in parallel using multiple processors or threads.

Key takeaways

Parallel mesh generation belongs to biology; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Parallel mesh generation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Parallel mesh generation from memory before moving on to harder problems.

Reference excerpt

Parallel mesh generation in numerical analysis is a new research area between the boundaries of two scientific computing disciplines: computational geometry and parallel computing. Parallel mesh generation methods decompose the original mesh generation problem into smaller subproblems which are solved (meshed) in parallel using multiple processors or threads. The existing parallel mesh generation methods can be classified in terms of two basic attributes:

the sequential technique used for meshing the individual subproblems and the degree of coupling between the subproblems. One of the challenges in parallel mesh generation is to develop parallel meshing software using off-the-shelf sequential meshing codes.

Overview Parallel mesh generation procedures in general decompose the original 2-dimensional (2D) or 3-dimensional (3D) mesh generation problem into N smaller subproblems which are solved (i.e., meshed) concurrently using P processors or threads. The subproblems can be formulated to be either tightly coupled, partially coupled or even decoupled. The coupling of the subproblems determines the intensity of the communication and the amount/type of synchronization required between the subproblems. The challenges in parallel mesh generation methods are: to maintain stability of the parallel mesher (i.e., retain the quality of finite elements generated by state-of-the-art sequential codes) and at the same time achieve 100% code re-use (i.e., leverage the continuously evolving and fully functional off-the-shelf sequential meshers) without substantial deterioration of the scalability of the parallel mesher. There is a difference between parallel mesh generation and parallel triangulation. In parallel triangulation a pre-defined set of points is used to generate in parallel triangles that cover the convex hull of the set of points. A very efficient algorithm for parallel Delaunay triangulations appears in Blelloch et al. This algorithm is extended in Clemens and Walkington for parallel mesh generation.

Parallel mesh generation software While many solvers have been ported to parallel machines, grid generators have left behind. Still the preprocessing step of mesh generation remains a sequential bottleneck in the simulation cycle. That is why the need for developing of stable 3D parallel grid generator is well-justified. A parallel version of the MeshSim mesh generator by Simmetrix Inc., is available for both research and commercial use. It includes parallel implementations of surface, volume and boundary layer mesh generation as well as parallel mesh adaptivity. The algorithms it uses are based on those in reference and are scalable (both in the parallel sense and in the sense that they give speedup compared to the serial implementation) and stable. For multicore or multiprocessor systems, there is also a multithreaded version of these algorithms that are available in the base MeshSim product Another parallel mesh generator is D3D, was developed by Daniel Rypl at Czech Technical University in Prague. D3D is a mesh generator capable to discretize in parallel (or sequentially) 3D domains into mixed meshes. BOXERMesh is an unstructured hybrid mesh generator developed by Cambridge Flow Solutions. Implemented as distributed-memory fully parallelised software, it is specifically designed to overcome the traditional bottlenecks constraining engineering simulation, delivering advanced meshing on geometries of arbitrary complexity and size. Its scalability has been demonstrated on very large meshes generated on HPC clusters.

Challenges in parallel mesh generation It takes substantial time to develop the algorithmic and software infrastructure for commercial sequential mesh generation libraries. Moreover, improvements in terms of quality, speed, and functionality are open ended which makes the task of creating leading edge parallel mesh generation codes challenging. An area with immediate high benefits to parallel mesh generation is domain decomposition. The DD problem as it is posed in is still open for 3D geometries and its solution will help to deliver stable and scalable methods that rely on off-the-shelf mesh generation codes for Delaunay and Advancing Front Techniques. Finally, a long term investment to parallel mesh generation is to attract the attention of mathematicians with open problems in mesh generation and broader impact in mathematics.

See also Mesh generation Parallel computing

References

Worked examples

Example 1 — a first encounter with Parallel mesh generation

Start with the simplest possible case. Write down what Parallel mesh generation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In biology, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Parallel mesh generation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Parallel mesh generation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Parallel mesh generation

In research: Parallel mesh generation appears in biology research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Parallel mesh generation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Parallel mesh generation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Mesh generation, Parallel computing, so understanding it makes those chapters shorter.
In everyday life: Look for Parallel mesh generation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Parallel mesh generation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Parallel mesh generation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Parallel mesh generation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Parallel mesh generation in simple terms?

Why does Parallel mesh generation matter?

Because it connects several biology ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Parallel mesh generation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Parallel mesh generation.