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 1 / 3

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, θ l (ˆ x ) − θ l (ˆ y ) } , l = 1 , 2 x 2 − 5 � 3 x 4 , l = 1 where θ l ( x ) := (1) x 2 − 25 6 x 4 + 7 2 x 6 , l = 2 The reference four DSSY degrees of freedom are given at the midpoints. Let F Q : ˆ Q → Q be a bijective affine transformation. Then v ∈ DSSY ( ˆ v ◦ F − 1 DSSY ( Q ) = { ˆ Q | ˆ Q ) } . Then DSSY FEM is defined by DSSY h = { v ∈ L 2 (Ω) | v | Q ∈ DSSY ( Q ) for all Q ∈ τ h ; v is continuous at the midpoint of each interior edge } 2 / 3

DSSY implementation on deal.II "solution.gpl" "solution-dssy .gpl" 0.3 0.3 0.25 0.25 0.2 0.2 0.15 0.15 0.1 0.1 0.05 0.05 0 0 -0.05 1 1 0.5 0.5 -1 -1 0 0 -0.5 -0.5 0 -0.5 0 -0.5 0.5 0.5 1-1 1-1 "solution-2d-org.gpl" "solution-2d-dssy .gpl" 2 2.2 2 1.8 1.8 1.6 1.6 1.4 1.4 1.2 1.2 1 1 1 1 0.5 0.5 -1 -1 0 0 -0.5 -0.5 0 -0.5 0 -0.5 0.5 0.5 1-1 1-1 Figure: (step3) Q 1 CFE / DSSY NCFE solution (step4) Q 1 CFE / DSSY NCFE solution Thing to do : Apply DSSY to other test problems ; Changes should be made in 3 / 3 nonconforming sense