Prolongation - Revision history

Rhaas: /* Useful references */

2024-01-24T15:23:22Z

‎Useful references

Rhaas: /* Useful references */

2023-12-13T13:48:17Z

‎Useful references

Rhaas: /* Useful references */

2023-12-13T13:40:57Z

‎Useful references

78.52.117.111: /* Use */

2017-09-19T17:41:37Z

‎Use

78.52.117.111: /* Update - 17-Aug-2017 */

2017-09-19T17:40:47Z

‎Update - 17-Aug-2017

Hinder: /* Call with Bishop - 17-Aug-2017 */

2017-08-17T15:26:04Z

‎Call with Bishop - 17-Aug-2017

Hinder: /* Update - 17-Aug-2017 */

2017-08-17T15:25:28Z

‎Update - 17-Aug-2017

Hinder: /* Useful references */

2017-08-17T15:23:52Z

‎Useful references

Hinder at 15:21, 17 August 2017

2017-08-17T15:21:37Z

Hinder: /* Meeting - 10-Aug-2017 */

2017-08-10T23:06:38Z

‎Meeting - 10-Aug-2017

@@ Line 18: / Line 18: @@
 * [https://www.sciencedirect.com/science/article/pii/S002199911500008X McCoquodale et al. - High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids]
 * [https://open.uct.ac.za/items/bfbb589d-35b5-4d7a-af17-b0e5db7c51ec/full Problems in cosmology and numerical relativity] (Bishop's PhD thesis)
 ==Meeting - 07-Aug-2017==

@@ Line 17: / Line 17: @@
 * [http://www.jstor.org/stable/2005559?origin=crossref Gustafsson - The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems] (one order lower at boundary)
 * [https://www.sciencedirect.com/science/article/pii/S002199911500008X McCoquodale et al. - High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids]
 ==Meeting - 07-Aug-2017==

@@ Line 16: / Line 16: @@
 * [http://www.sciencedirect.com/science/article/pii/S0021999111000908?via%3Dihub Shen - Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations]
 * [http://www.jstor.org/stable/2005559?origin=crossref Gustafsson - The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems] (one order lower at boundary)
 ==Meeting - 07-Aug-2017==

@@ Line 156: / Line 156: @@
 * Set these parameters:
 ** Carpet::use_buffer_zones                = no
 ** MoL::rk_prolongation                    = yes

←Older revision		Revision as of 17:40, 19 September 2017
Line 150:		Line 150:
	* See numerical blowups with 3 levels with the wave equation. Suspect that we need to smooth out the sharp features at the refinement boundaries.		* See numerical blowups with 3 levels with the wave equation. Suspect that we need to smooth out the sharp features at the refinement boundaries.
	* Next step: implement transition zones from Bishop's paper		* Next step: implement transition zones from Bishop's paper
		+
		+	==Use==
		+
		+	* Use the rkprol branches of Carpet and MoL
		+	* Set these parameters:
		+	** Carpet::use_buffer_zones = no
		+	** MoL::disable_prolongation = yes
		+	** MoL::rk_prolongation = yes

@@ Line 115: / Line 115: @@
 == Call with Bishop - 17-Aug-2017 ==
-Most papers focused on RK methods.  Other arguments for other methods.  Errors cancel, so one order lower is ok.
+* Most papers focused on RK methods.  Other arguments for other methods.  Errors cancel, so one order lower is ok.
-interpolants for rk formulae
+* 1996 interpolants for rk formulae
-carpetner - wave eq in 2nd order, 3rd at boundary but reported 4th order.
+* carpetner - wave eq in 2nd order, 3rd at boundary but reported 4th order.
-carpetner - jacobian term helps to get the nonlinear system
+* carpetner - jacobian term helps to get the nonlinear system.  bishop thessis chapter 9 - put in jacobian by hand - for carpenter.  for unigrid.  gowdy wave.  adm geodesic.
-order reduction - error propagates inwards!  bdr has to be consistent.
+* order reduction - error propagates inwards!  bdr has to be consistent.
-special case of sponge boundary
+* special case of sponge boundary
-difference is sponge applied at every substep
+* difference is sponge applied at every substep
-tz applied at end of fine step. (maybe)
+* tz applied at end of fine step. (maybe)
-need coarse grid approxes.  soln for fine grid and coarse grid at same time - linear interpolation of grids.  weight factor in linear interpolation gives smoothness - 3 transition zones - same thing.
+* need coarse grid approxes.  soln for fine grid and coarse grid at same time - linear interpolation of grids.  weight factor in linear interpolation gives smoothness - 3 transition zones - same thing.  speed of prop depends on size of grid.  mode speed changes abruptly cand causes refelctions.  reduces reflections.
-sponge boundary can be as large as you need and use in restriction, but with transition zone, need to exclude transition from restriction - instabilities.
+* sponge boundary can be as large as you need and use in restriction, but with transition zone, need to exclude transition from restriction - instabilities.
-interpolation is done using ks, ths, bs.  can generate the ys
+* interpolation is done using ks, ths, bs.  can generate the ys
-also communicates the yn.  so need 6 variables.  just need yns, but keep other because it is solution.
+* also communicates the yn.  so need 6 variables.  just need yns, but keep other because it is solution.
-he has yn and yn+1 because he needs yn+1 anyway. we can use just yn from the coarse grid - need to prolongate one more variable.
+* he has yn and yn+1 because he needs yn+1 anyway. we can use just yn from the coarse grid - need to prolongate one more variable.
 ==Update - 17-Aug-2017==

←Older revision		Revision as of 15:25, 17 August 2017
Line 111:		Line 111:

	* Continue with implementation of RK prolongation in MoL		* Continue with implementation of RK prolongation in MoL
		+
		+
		+	== Call with Bishop - 17-Aug-2017 ==
		+
		+	Most papers focused on RK methods. Other arguments for other methods. Errors cancel, so one order lower is ok.
		+
		+	1996 interpolants for rk formulae
		+
		+	carpetner - wave eq in 2nd order, 3rd at boundary but reported 4th order.
		+
		+	carpetner - jacobian term helps to get the nonlinear system
		+	bishop thessis chapter 9 - put in jacobian by hand - for carpenter. for unigrid. gowdy wave. adm geodesic.
		+
		+	order reduction - error propagates inwards! bdr has to be consistent.
		+
		+	special case of sponge boundary
		+
		+	difference is sponge applied at every substep
		+
		+	tz applied at end of fine step. (maybe)
		+
		+	need coarse grid approxes. soln for fine grid and coarse grid at same time - linear interpolation of grids. weight factor in linear interpolation gives smoothness - 3 transition zones - same thing.
		+	speed of prop depends on size of grid. mode speed changes abruptly cand causes refelctions. reduces reflections.
		+
		+	sponge boundary can be as large as you need and use in restriction, but with transition zone, need to exclude transition from restriction - instabilities.
		+
		+	interpolation is done using ks, ths, bs. can generate the ys
		+
		+	also communicates the yn. so need 6 variables. just need yns, but keep other because it is solution.
		+
		+	he has yn and yn+1 because he needs yn+1 anyway. we can use just yn from the coarse grid - need to prolongate one more variable.

	==Update - 17-Aug-2017==		==Update - 17-Aug-2017==

←Older revision		Revision as of 15:21, 17 August 2017
Line 110:		Line 110:

	* Continue with implementation of RK prolongation in MoL		* Continue with implementation of RK prolongation in MoL
		+
		+	==Update - 17-Aug-2017==
		+
		+	* Code implemented and tested for 2-level system
		+	* Gauge wave and FTSS wave equation give 4th order convergence at low resolution, but convergence is not perfect at high resolution. Could be dropping to 3rd order there.
		+	* Fully first order wave equation gives clean 4th order convergence at all resolutions
		+	* Second derivatives need higher regularity of the solution; maybe they are spoiled by the sharp features introduced by RBs.
		+	* Code extended to arbitrary number of refinement levels
		+	* See numerical blowups with 3 levels with the wave equation. Suspect that we need to smooth out the sharp features at the refinement boundaries.
		+	* Next step: implement transition zones from Bishop's paper

@@ Line 92: / Line 92: @@
 Ian:
-* Started implementing RK prolongation in Cactus.  All implementation should be in MoL.  Needed to fix a problem in Carpet relating to the "copy" prolongation operator.  Currently have the ks prolongated, and the ks copied into the kTildes.  Working on setting the RHS vars in the refinement boundaries from the kTildes.
+* Started implementing RK prolongation in Cactus.  All implementation should be in MoL.
 ===Tasks for next meeting===
@@ Line 98: / Line 101: @@
 Roland:
-* Will test prolongation implemented by Ian
+* Will test prolongation implemented by Ian actually works, with op_copy.
 Eloisa: