Triangulation No of elements = 16 No of nodes = 13 No interior nodes = 5 No of boundary nodes = 8

  • View
    213

  • Download
    1

Embed Size (px)

Text of Triangulation No of elements = 16 No of nodes = 13 No interior nodes = 5 No of boundary nodes = 8

  • Slide 1
  • Triangulation No of elements = 16 No of nodes = 13 No interior nodes = 5 No of boundary nodes = 8
  • Slide 2
  • With the triangulation we associate the function space consisting of continuous, piecewise linear functions on vanishing on i.e Triangulation No interior nodes = 5 No of global basis functions = 5
  • Slide 3
  • 1 2 3 4 5 6 7 8 9 10 11 12 13 Element Labeling 14 15 16
  • Slide 4
  • Node Labeling (global labeling) 12 34 5 6 7 8 9 1011 1213
  • Slide 5
  • global basis functions 12 34 5 6 7 8 9 1011 1213
  • Slide 6
  • 12 34 5 6 7 8 9 1011 1213 global basis functions
  • Slide 7
  • Global basis functions
  • Slide 8
  • global basis functions 12 34 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 1011 5 1312
  • Slide 9
  • 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
  • Slide 10
  • global basis functions 12 34 6 7 8 9 0 0 0 0 0 0 0 0 1011 5 1312 0 0
  • Slide 11
  • 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 12 34 5 6 7 8 9 1011 1213 Assemble linear system
  • Slide 12
  • 12 34 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 1011 5 1312 12 34 6 7 8 9 0 0 0 0 0 0 0 0 1011 5 1312 0 0
  • Slide 13
  • Approximation of u 01 02 03 04 0.0695 06 07 08 09 0.04910 0.04911 0.04912 0.04913
  • Slide 14
  • Node Label (local labeling) 12 3 Each triangle has 3 nodes. Label them locally inside the triangle
  • Slide 15
  • Node and Element Label
  • Slide 16
  • Local label.vs. global label Matrix t(3,#elements) 16151413121110987654321 131211105555432132141 1211101312111013 12111087692 8769131211108769121110133
  • Slide 17
  • X-coordinate and y-coordinate Matrix p(2,#elements) 13121110987654321 0.750.25 0.7510.50 1001x 0.25 0.75 0.50 1 0011y
  • Slide 18
  • Boundary node vector e(#boundary node) e8e7e6e5e4e3e2e1 98764321start 14329876end
  • Slide 19
  • Approximation of u 01 02 03 04 0.0695 06 07 08 09 0.04910 0.04911 0.04912 0.04913
  • Slide 20
  • Global basis functions
  • Slide 21
  • Triangulation