Transform integrals onto the unit square
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Let $t$ denote an arbitrary triangle in the 2-dimensional mesh and let $hat{t}$ denote the reference triangle. Given are also two integrals: $$I_t(g) = int_t g(x) dx $$ and $$J_t(g) = int_t nabla g(x) dx $$ for $x in mathbb R^2$.
Now, if $$phi: (0,1)^2 to hat{t} $$ $$(epsilon, n) to (epsilon, (1-epsilon) n)$$
Can anyone transform the integrals $I_t$ and $J_t$ onto the unit square via $hat{t}$ ?
geometry numerical-methods transformation
asked 12 hours ago
StMan
1337
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up vote
0
down vote
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Let $t$ denote an arbitrary triangle in the 2-dimensional mesh and let $hat{t}$ denote the reference triangle. Given are also two integrals: $$I_t(g) = int_t g(x) dx $$ and $$J_t(g) = int_t nabla g(x) dx $$ for $x in mathbb R^2$.
Now, if $$phi: (0,1)^2 to hat{t} $$ $$(epsilon, n) to (epsilon, (1-epsilon) n)$$
Can anyone transform the integrals $I_t$ and $J_t$ onto the unit square via $hat{t}$ ?
geometry numerical-methods transformation
asked 12 hours ago
StMan
1337
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $t$ denote an arbitrary triangle in the 2-dimensional mesh and let $hat{t}$ denote the reference triangle. Given are also two integrals: $$I_t(g) = int_t g(x) dx $$ and $$J_t(g) = int_t nabla g(x) dx $$ for $x in mathbb R^2$.
Now, if $$phi: (0,1)^2 to hat{t} $$ $$(epsilon, n) to (epsilon, (1-epsilon) n)$$
Can anyone transform the integrals $I_t$ and $J_t$ onto the unit square via $hat{t}$ ?
geometry numerical-methods transformation
asked 12 hours ago
StMan
1337
Let $t$ denote an arbitrary triangle in the 2-dimensional mesh and let $hat{t}$ denote the reference triangle. Given are also two integrals: $$I_t(g) = int_t g(x) dx $$ and $$J_t(g) = int_t nabla g(x) dx $$ for $x in mathbb R^2$.
Now, if $$phi: (0,1)^2 to hat{t} $$ $$(epsilon, n) to (epsilon, (1-epsilon) n)$$
Can anyone transform the integrals $I_t$ and $J_t$ onto the unit square via $hat{t}$ ?
geometry numerical-methods transformation
geometry numerical-methods transformation
asked 12 hours ago
StMan
1337
asked 12 hours ago
StMan
1337
asked 12 hours ago
StMan
1337
asked 12 hours ago
StMan
1337
asked 12 hours ago
StMan
1337
1337
add a comment |
add a comment |
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