From a3858bb797a7e3bd6156dc5499bb2a69e5742dae Mon Sep 17 00:00:00 2001
From: Bruno Seny <bruno.seny@student.uclouvain.be>
Date: Thu, 11 Mar 2010 16:09:48 +0000
Subject: [PATCH] Butcher tables becomes static, RK22 is not yet conservative
....
---
Solver/dgRungeKuttaMultirate.cpp | 149 +++++++++++++++++--------------
1 file changed, 83 insertions(+), 66 deletions(-)
diff --git a/Solver/dgRungeKuttaMultirate.cpp b/Solver/dgRungeKuttaMultirate.cpp
index ad35b10a62..ee67970e8d 100644
--- a/Solver/dgRungeKuttaMultirate.cpp
+++ b/Solver/dgRungeKuttaMultirate.cpp
@@ -9,7 +9,7 @@
#include <stdio.h>
//#define MULTIRATEVERBOSE
-
+//Butcher tables for RK43 (Schlegel)
static double A43[4][4]={
{0, 0, 0, 0},
{1.0/2.0, 0, 0 ,0},
@@ -43,12 +43,39 @@ static double AOuter43[10][10]={
{1.0/3.0 , 0, 0, 0, -1.0/3.0, 1, 0, 0, 0, 0},
};
-static double b[4]={1.0/6.0, 1.0/3.0, 1.0/3.0, 1.0/6.0};
-static double c[4]={0, 1.0/2.0, 1.0/2.0, 1};
-static double bInner[10]={1.0/12.0, 1.0/6.0, 1.0/6.0,1.0/12.0,0,1.0/12.0, 1.0/6.0, 1.0/6.0,1.0/12.0,0};
-static double cInner[10]={0, 1.0/4.0, 1.0/4.0, 1.0/2.0, 1.0/2.0, 1.0/2.0, 3.0/4.0, 3.0/4.0, 1, 1 };
-static double bOuter[10]={1.0/6.0, 0 , 0 , 0 , 1.0/3.0,1.0/3.0, 0 , 0 , 0 , 1.0/6.0};
-static double cOuter[10]={0, 1.0/4.0, 1.0/4.0, 1.0/2.0, 1.0/2.0, 1.0/2.0, 3.0/4.0, 3.0/4.0, 1, 1 };
+static double b43[4]={1.0/6.0, 1.0/3.0, 1.0/3.0, 1.0/6.0};
+static double c43[4]={0, 1.0/2.0, 1.0/2.0, 1};
+static double bInner43[10]={1.0/12.0, 1.0/6.0, 1.0/6.0,1.0/12.0,0,1.0/12.0, 1.0/6.0, 1.0/6.0,1.0/12.0,0};
+static double cInner43[10]={0, 1.0/4.0, 1.0/4.0, 1.0/2.0, 1.0/2.0, 1.0/2.0, 3.0/4.0, 3.0/4.0, 1, 1 };
+static double bOuter43[10]={1.0/6.0, 0 , 0 , 0 , 1.0/3.0,1.0/3.0, 0 , 0 , 0 , 1.0/6.0};
+static double cOuter43[10]={0, 1.0/4.0, 1.0/4.0, 1.0/2.0, 1.0/2.0, 1.0/2.0, 3.0/4.0, 3.0/4.0, 1, 1 };
+
+// Butcher tables for Multirate RK22 (Constantinescu)
+static double A22[2][2]={
+ {0, 0},
+ {1.0, 0}
+ };
+ // Small step RK22
+static double AInner22[4][4]={
+ {0, 0, 0, 0},
+ {1.0/2.0, 0, 0, 0},
+ {1.0/4.0, 1.0/4.0, 0, 0},
+ {1.0/4.0, 1.0/4.0, 1.0/2.0, 0}
+ };
+
+ // Big step RK22
+static double AOuter22[4][4]={
+ {0, 0, 0, 0},
+ {1.0, 0, 0, 0},
+ {0, 0, 0, 0},
+ {0, 0, 1.0, 0}
+ };
+static double b22[2]={1.0/2.0, 1.0/2.0};
+static double c22[2]={0, 1.0};
+static double bInner22[4]={1.0/4.0, 1.0/4.0, 1.0/4.0, 1.0/4.0};
+static double cInner22[4]={0, 1.0/2.0, 1.0/2.0, 1.0};
+static double bOuter22[4]={1.0/4.0, 1.0/4.0, 1.0/4.0, 1.0/4.0};
+static double cOuter22[4]={0, 1.0, 0, 1.0};
dgRungeKuttaMultirate::dgRungeKuttaMultirate(dgGroupCollection* gc,dgConservationLaw *law, int nStages){
_law=law;
@@ -416,17 +443,17 @@ void dgRungeKuttaMultirate43::updateSolution(int exponent,bool isBuffer){
std::vector<dgGroupOfElements *>&gVi=_innerBufferGroupsOfElements[exponent].first;
std::vector<dgGroupOfElements *>&gVo=_outerBufferGroupsOfElements[exponent].first;
for(int i=0;i<10;i++){
- if(bInner[i]!=0.0)
- _solution->axpy(gVi,*_K[i],bInner[i]*localDt*2);
- if(bOuter[i]!=0.0)
- _solution->axpy(gVo,*_K[i],bOuter[i]*localDt*2);
+ if(bInner43[i]!=0.0)
+ _solution->axpy(gVi,*_K[i],bInner43[i]*localDt*2);
+ if(bOuter43[i]!=0.0)
+ _solution->axpy(gVo,*_K[i],bOuter43[i]*localDt*2);
}
}
else{
std::vector<dgGroupOfElements *>&gV=_bulkGroupsOfElements[exponent].first;
for(int i=0;i<4;i++){
- if(b[i]!=0.0)
- _solution->axpy(gV,*_K[i],b[i]*localDt);
+ if(b43[i]!=0.0)
+ _solution->axpy(gV,*_K[i],b43[i]*localDt);
}
_currentInput->scale(gV,0.0);
_currentInput->axpy(gV,*_solution,1.0);
@@ -463,29 +490,19 @@ void dgRungeKuttaMultirate22::computeInputForK(int iK,int exponent,bool isBuffer
return;
}
double localDt=_dt/pow(2.0,(double)exponent);
- double _A[2][2]={
- {0, 0},
- {1.0, 0}
- };
- // Small step RK22
- double _AInner[4][4]={
- {0, 0, 0, 0},
- {1.0/2.0, 0, 0, 0},
- {1.0/4.0, 1.0/4.0, 0, 0},
- {1.0/4.0, 1.0/4.0, 1.0/2.0, 0}
- };
-
- // Big step RK22
- double _AOuter[4][4]={
- {0, 0, 0, 0},
- {1.0, 0, 0, 0},
- {0, 0, 0, 0},
- {0, 0, 1.0, 0}
- };
-
// compute K[iK] for this exponent and buffer
- if(isBuffer){
+ if(!isBuffer){
+ std::vector<dgGroupOfElements *> &gV=_bulkGroupsOfElements[exponent].first;
+ _currentInput->scale(gV,0.0);
+ _currentInput->axpy(gV,*_solution,1.0);
+ for(int i=0;i<iK;i++){
+ if(A22[iK][i]!=0.0){
+ _currentInput->axpy(gV,*_K[i],A22[iK][i]*localDt);
+ }
+ }
+ }
+ else{
std::vector<dgGroupOfElements *>&gVi=_innerBufferGroupsOfElements[exponent].first;
std::vector<dgGroupOfElements *>&gVo=_outerBufferGroupsOfElements[exponent].first;
_currentInput->scale(gVi,0.0);
@@ -493,20 +510,10 @@ void dgRungeKuttaMultirate22::computeInputForK(int iK,int exponent,bool isBuffer
_currentInput->axpy(gVi,*_solution,1.0);
_currentInput->axpy(gVo,*_solution,1.0);
for(int i=0;i<iK;i++){
- if(_AInner[iK][i]!=0.0){
- _currentInput->axpy(gVi,*_K[i],_AInner[iK][i]*localDt*2);}
- if(_AOuter[iK][i]!=0.0)
- _currentInput->axpy(gVo,*_K[i],_AOuter[iK][i]*localDt*2);
- }
- }
- else{
- std::vector<dgGroupOfElements *> &gV=_bulkGroupsOfElements[exponent].first;
- _currentInput->scale(gV,0.0);
- _currentInput->axpy(gV,*_solution,1.0);
- for(int i=0;i<iK;i++){
- if(_A[iK][i]!=0.0){
- _currentInput->axpy(gV,*_K[i],_A[iK][i]*localDt);
- }
+ if(AInner22[iK][i]!=0.0){
+ _currentInput->axpy(gVi,*_K[i],AInner22[iK][i]*localDt*2);}
+ if(AOuter22[iK][i]!=0.0)
+ _currentInput->axpy(gVo,*_K[i],AOuter22[iK][i]*localDt*2);
}
}
@@ -523,46 +530,56 @@ void dgRungeKuttaMultirate22::computeInputForK(int iK,int exponent,bool isBuffer
else{
computeInputForK(iK%2,exponent,false);
}
- computeK(iK,exponent,isBuffer);
- // Msg::Info("Multirate %d %0.16e",iK,_K[iK]->norm());
- if( (iK==1 && !isBuffer) || (iK==3 && isBuffer) ){
- updateSolution(exponent,isBuffer);
- }
- if(!isBuffer){
+
+ if(exponent==0){
+ computeK(iK, exponent, false);
switch(iK){
case 0:
for(int i=1;i<3;i++){
computeInputForK(i,exponent+1,true);
}
break;
+ case 1:
+ updateSolution(exponent, false);
+ break;
+ }
+ }
+
+ if(isBuffer && exponent>0){
+ computeK(iK%2, exponent, false);
+ computeK(iK, exponent, true);
+ if(iK%2==1)
+ updateSolution(exponent, false);
+ if(iK==3)
+ updateSolution(exponent, true);
+ switch(iK){
+ case 0:
+ for(int i=1;i<3;i++){
+ computeInputForK(i, exponent+1, true);
}
+ break;
}
+ }
}
void dgRungeKuttaMultirate22::updateSolution(int exponent,bool isBuffer){
//Msg::Info("Updating solution at level %d %s",exponent,isBuffer?"Buffer":"Bulk");
double localDt=_dt/pow(2.0,(double)exponent);
- double b[2]={1.0/2.0, 1.0/2.0};
- double c[2]={0, 1.0};
- double bInner[4]={1.0/4.0, 1.0/4.0, 1.0/4.0, 1.0/4.0};
- double cInner[4]={0, 1.0/2.0, 1.0/2.0, 1.0};
- double bOuter[4]={1.0/4.0, 1.0/4.0, 1.0/4.0, 1.0/4.0};
- double cOuter[4]={0, 1.0, 0, 1.0};
if(isBuffer){
std::vector<dgGroupOfElements *>&gVi=_innerBufferGroupsOfElements[exponent].first;
std::vector<dgGroupOfElements *>&gVo=_outerBufferGroupsOfElements[exponent].first;
for(int i=0;i<4;i++){
- if(bInner[i]!=0.0)
- _solution->axpy(gVi,*_K[i],bInner[i]*localDt*2);
- if(bOuter[i]!=0.0)
- _solution->axpy(gVo,*_K[i],bOuter[i]*localDt*2);
+ if(bInner22[i]!=0.0)
+ _solution->axpy(gVi,*_K[i],bInner22[i]*localDt*2);
+ if(bOuter22[i]!=0.0)
+ _solution->axpy(gVo,*_K[i],bOuter22[i]*localDt*2);
}
}
else{
std::vector<dgGroupOfElements *>&gV=_bulkGroupsOfElements[exponent].first;
for(int i=0;i<2;i++){
- if(b[i]!=0.0)
- _solution->axpy(gV,*_K[i],b[i]*localDt);
+ if(b22[i]!=0.0)
+ _solution->axpy(gV,*_K[i],b22[i]*localDt);
}
}
}
--
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