DSSY implementation on deal. II Imbunm Kim Seoul National University - - PowerPoint PPT Presentation

DSSY implementation on deal. II

Imbunm Kim

Seoul National University ibkim11@gmail.com

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DSSY Nonconforming Quadrilateral Finite Element (RAIRO Anam. Numer. 33, 1999, Douglas-Santos-Sheen-Ye) On a reference domain ˆ Q := [−1, 1]2, define DSSY ( ˆ Q) = span{1, ˆ x, ˆ y, θl(ˆ x) − θl(ˆ y)}, l = 1, 2 where θl(x) :=

• x2 − 5

3x4,

l = 1 x2 − 25

6 x4 + 7 2x6,

l = 2 (1) The reference four DSSY degrees of freedom are given at the midpoints. Let FQ : ˆ Q → Q be a bijective affine transformation. Then DSSY (Q) = {ˆ v ◦ F −1

Q |ˆ

v ∈ DSSY ( ˆ Q)}. Then DSSY FEM is defined by DSSY h = {v ∈ L2(Ω)|v|Q ∈ DSSY (Q) for allQ ∈ τh; v is continuous at the midpoint of each interior edge}

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DSSY implementation on deal.II

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0.5 1-1

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0.5 1 0.05 0.1 0.15 0.2 0.25 0.3 "solution.gpl"

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0.5 1-1

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0.5 1

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0.05 0.1 0.15 0.2 0.25 0.3 "solution-dssy .gpl"

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0.5 1-1

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0.5 1 1 1.2 1.4 1.6 1.8 2 "solution-2d-org.gpl"

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0.5 1-1

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0.5 1 1 1.2 1.4 1.6 1.8 2 2.2 "solution-2d-dssy .gpl"

Figure: (step3) Q1 CFE / DSSY NCFE solution

(step4) Q1 CFE / DSSY NCFE solution

Thing to do : Apply DSSY to other test problems ; Changes should be made in nonconforming sense

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