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The Multilevel Grid Data Structure

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Outline
1. Introduction
2. Adaptive Modification
3. Integrated Legendre Projection
4. Example

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What is a Multilevel Grid ?
A Data Structure that ...
• is based on spacetree partitioning
• stores cells on separate grids at different levels
• is highly generic due to templetized cell data
• uses simple indexing to identify and navigate between cells

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expand and collapse

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Storage of cells
• cells are stored on each separate grid with no direct connection to
their respective parent cells
• on each grid a hash table is used to enable a fast access to each
cell

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Basic Structure

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The Hash Function

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General
Two major steps where needed to install real adaptivity
– Adaptive Topology: Implementing refinement strategies to
consciously steer the expanding and collapsing of cells
– Data Projection: preserve and extend data between time steps and
across the changing grids

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Topology
Refinement Strategies
– Differentiates cells into cells to
expand and cells to collapse
– many different strategies of
refinement
– Implemented as a strategy pattern

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Refinement Strategies

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Data Projection
• preserve data over changing grids
– history variables
• Generic structure
– strategy pattern

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AdhoC++ Framework

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Integrated Legendre Projection
• based on integrated Legendre
polynomials
• cells are storing coefficients
– std::vector<double>
• local definition of basis
polynomials

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Linear system of equations

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Projection between grids

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Moving Heat Source 2d
Moving heat source equation:
Refinement Strategy:
RefineElementsInsideSphere

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Convergence Study

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Moving Wave Front 2d
Wave equation:
Refinement Strategy:
RefineTowardsGradient

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Convergence Study

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Thank you for your attention