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Added: 3D LR adaptivity benchmark cases #15

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3ff03ed
fixed: make sure to resize projections
akva2 Oct 17, 2017
da58565
Added: 3D LR adaptivity benchmark cases
VikingScientist Oct 17, 2017
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81 changes: 81 additions & 0 deletions Adaptive_benchmark/ArctanSphericalWaveFront.xinp
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<?xml version="1.0" encoding="UTF-8" standalone="yes"?>

<!--*************************************************************

Arctan Spherical Wave Front


(http://math.nist.gov/cgi-bin/amr-display-problem.cgi)

-nabla^2(u) = f, in Omega
u = g, on Gamma

Omega : (0,1)^3

Exact solution: u = atan(alpha*(r-r0))
r = sqrt((x-x0)^2 + (y-y0)^2 + (z-z0)^2)
Parameters: (x0,y0,z0) center of the spherical wave front
r0 radius of the cirular wave front
alpha controls the steepness of the wave front

Parameter Reccomendations:
- Mild wave front
(x0,y0,z0) = (-.05 ,-.05, -.05)
r0 = 0.7
alpha = 20

- Steep wave front
(x0,y0,z0) = (-.05 ,-.05, -.05)
r0 = 0.7
alpha = 1000

**********************************************************************-->


<simulation>

<!-- General - geometry definitions !-->
<geometry sets="true">
<raiseorder patch="1" u="1" v="1" w="1"/>
<refine patch="1" u="7" v="7" w="7"/>
</geometry>

<!-- General - boundary conditions !-->
<boundaryconditions>
<dirichlet set="Boundary" comp="1" type="anasol"/>
</boundaryconditions>

<postprocessing>
<vtfformat nu="2" nv="2" nw="2">BINARY</vtfformat>
</postprocessing>

<!-- Problem-specific block !-->
<poisson>
<source type="expression"> x0=-.05; y0=-.05; z0=-.05; r=sqrt(pow(x-x0,2)+pow(y-y0,2)+pow(z-z0,2)); alpha=20; r0=0.7;

(alpha*(2*x - 2*x0)^2)/(4*(alpha^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2))^2 + 1)*((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(3/2)) - (3*alpha)/((alpha^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2))^2 + 1)*((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2)) + (alpha*(2*y - 2*y0)^2)/(4*(alpha^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2))^2 + 1)*((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(3/2)) + (alpha*(2*z - 2*z0)^2)/(4*(alpha^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2))^2 + 1)*((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(3/2)) - (alpha^3*(2*z - 2*z0)^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2)))/(2*(alpha^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2))^2 + 1)^2*((x - x0)^2 + (y - y0)^2 + (z - z0)^2)) - (alpha^3*(2*x - 2*x0)^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2)))/(2*(alpha^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2))^2 + 1)^2*((x - x0)^2 + (y - y0)^2 + (z - z0)^2)) - (alpha^3*(2*y - 2*y0)^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2)))/(2*(alpha^2*(r0 - ((x - x0)^2 + (y - y0)^2 + (z - z0)^2)^(1/2))^2 + 1)^2*((x - x0)^2 + (y - y0)^2 + (z - z0)^2))

</source>
<anasol type="expression">
<variables> x0=-.05; y0=-.05; z0=-.05; r=sqrt(pow(x-x0,2)+pow(y-y0,2)+pow(z-z0,2)); alpha=20; r0=0.7 </variables>

<primary> atan(alpha*(r-r0)) </primary>
<secondary> -(alpha*(2*x - 2*x0))*pow(2*(alpha*alpha*pow(r - r0,2)+ 1)*r*r, -0.5) |
-(alpha*(2*y - 2*y0))*pow(2*(alpha*alpha*pow(r - r0,2)+ 1)*r*r, -0.5) |
-(alpha*(2*z - 2*z0))*pow(2*(alpha*alpha*pow(r - r0,2)+ 1)*r*r, -0.5)
</secondary>
</anasol>
</poisson>


<!--General - adaptive refinement parameters -->
<adaptive>
<maxstep>3</maxstep>
<beta type="AVERAGE">100</beta>
<maxdof>10000</maxdof>
<errtol>0.000001</errtol>
<knot_mult>1</knot_mult>
<scheme>isotropic_function</scheme>
</adaptive>

</simulation>
112 changes: 112 additions & 0 deletions Adaptive_benchmark/Fischera.g2
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108 changes: 108 additions & 0 deletions Adaptive_benchmark/FischeraCorner.xinp
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<?xml version="1.0" encoding="UTF-8" standalone="yes"?>

<!--*************************************************************

Fischera Corner with Vertex Singularity


(http://math.nist.gov/cgi-bin/amr-display-problem.cgi)

-nabla^2(u) = f, in Omega
u = g, on Gamma

Omega : (-1,1)^3 \ [0,1)^3

Exact solution: u = r^q
Parameters: q > -0.5 determines the strength of the singularity

**********************************************************************-->

<simulation>

<!-- General - geometry definitions !-->
<geometry>
<patchfile>Fischera.g2</patchfile>
<!--
-->
<raiseorder lowerpatch="1" upperpatch="7" u="1" v="1" w="1"/>
<refine lowerpatch="1" upperpatch="7" u="3" v="3" w="3"/>

<topology>
<connection master="5" mface="6" slave="6" sface="5"/>
<connection master="5" mface="4" slave="7" sface="3"/>
<connection master="3" mface="6" slave="4" sface="5"/>
<connection master="3" mface="2" slave="7" sface="1"/>
<connection master="2" mface="4" slave="4" sface="3"/>
<connection master="2" mface="2" slave="6" sface="1"/>
<connection master="1" mface="6" slave="2" sface="5"/>
<connection master="1" mface="4" slave="3" sface="3"/>
<connection master="1" mface="2" slave="5" sface="1"/>
</topology>

<topologysets>
<set name="Boundary" type="face">
<item patch="7">6</item>
<item patch="7">5</item>
<item patch="7">4</item>
<item patch="7">2</item>
<item patch="6">6</item>
<item patch="6">4</item>
<item patch="6">3</item>
<item patch="6">2</item>
<item patch="5">5</item>
<item patch="5">4</item>
<item patch="5">3</item>
<item patch="5">2</item>
<item patch="4">6</item>
<item patch="4">4</item>
<item patch="4">2</item>
<item patch="4">1</item>
<item patch="3">5</item>
<item patch="3">4</item>
<item patch="3">1</item>
<item patch="2">6</item>
<item patch="2">3</item>
<item patch="2">1</item>
<item patch="1">5</item>
<item patch="1">3</item>
<item patch="1">2</item>
<item patch="1">1</item>
</set>
</topologysets>

</geometry>

<!-- General - boundary conditions !-->
<boundaryconditions>
<dirichlet set="Boundary" comp="1" type="anasol"/>
</boundaryconditions>

<postprocessing>
<vtfformat nu="2" nv="2" nw="2">BINARY</vtfformat>
</postprocessing>

<!-- Problem-specific block !-->
<poisson>
<source type="expression">r2=(x*x+y*y+z*z); q=0.5; -q*(q+1)*pow(r2,q/2-1)</source>
<anasol type="expression">
<primary> r =sqrt(x*x + y*y + z*z); q=0.5; pow(r,q) </primary>
<secondary>r2= (x*x + y*y + z*z); q=0.5; -q*x*pow(r2,q/2 - 1) |
r2= (x*x + y*y + z*z); q=0.5; -q*y*pow(r2,q/2 - 1) |
r2= (x*x + y*y + z*z); q=0.5; -q*z*pow(r2,q/2 - 1)
</secondary>
</anasol>

</poisson>


<!--General - adaptive refinement parameters -->
<adaptive>
<maxstep>4</maxstep>
<beta type="AVERAGE">100</beta>
<maxdof>100000</maxdof>
<errtol>0.000001</errtol>
<knot_mult>1</knot_mult>
<scheme>isotropic_function</scheme>
</adaptive>

</simulation>
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