From 8cf7196c201029b1ee82befb6b73a63c8d8f1ab1 Mon Sep 17 00:00:00 2001
From: Florian Atteneder <florian.atteneder@uni-jena.de>
Date: Tue, 20 Aug 2024 13:18:45 +0000
Subject: [PATCH] ScalarEq: Implement modal Bspline2 DG evolution
 (https://git.tpi.uni-jena.de/dg/dg1d.jl/-/merge_requests/213)

Similar to !207, but using the new 2nd order Bspline basis.

Currently supports only bare evolutions and no HRSC etc.

Also: This is a quasi-nodal Ansatz similar to the Bernstein Ansatz, i.e. it is not interpolating, but the modal coefficients are related to some sampling of the data on the grid.
This means that one has to sum the modal coefficients onto the grid to obtain the nodal values, which can be done with `interpolate` or a Vandermonde matrix.
Atm this is not consistently done in the ScalarEq project, hence, care needs to be examined when interpreting results!
---
 src/ScalarEq/rhs.jl                           |  51 ++++++++++++++----
 src/ScalarEq/setup.jl                         |  11 +++-
 src/bspline.jl                                |   5 +-
 .../modal_bspline2_advection_sine.toml        |  21 ++++++++
 .../modal_bspline2_advection_sine/output1d.h5 | Bin 0 -> 114536 bytes
 .../substep_output.h5                         | Bin 0 -> 75944 bytes
 test/IntegrationTests/refs/testconfig.toml    |   3 ++
 7 files changed, 79 insertions(+), 12 deletions(-)
 create mode 100644 test/IntegrationTests/refs/modal_bspline2_advection_sine/modal_bspline2_advection_sine.toml
 create mode 100644 test/IntegrationTests/refs/modal_bspline2_advection_sine/output1d.h5
 create mode 100644 test/IntegrationTests/refs/modal_bspline2_advection_sine/substep_output.h5

diff --git a/src/ScalarEq/rhs.jl b/src/ScalarEq/rhs.jl
index 75100c42..8f4f038a 100644
--- a/src/ScalarEq/rhs.jl
+++ b/src/ScalarEq/rhs.jl
@@ -268,21 +268,54 @@ end
 
 
 function rhs!(env, mesh::Mesh1d, P::Project, hrsc::Nothing)
+  if mesh.element.kind === :modal_bspline2
+    modal_rhs!(env, mesh, P, hrsc)
+  else
+    nodal_rhs!(env, mesh, P, hrsc)
+  end
+end
 
-  @unpack cache, mesh = env
-  @unpack equation = P
 
-  @unpack flx_u, src_u   = get_static_variables(cache)
-  @unpack u              = get_dynamic_variables(cache)
-  @unpack rhs_u          = get_rhs_variables(cache)
-  @unpack nflx_u, bdry_u = get_bdry_variables(cache)
+function nodal_rhs!(env, mesh::Mesh1d, P::Project, hrsc::Nothing)
+  @unpack flx_u, src_u   = get_static_variables(mesh)
+  @unpack u              = get_dynamic_variables(mesh)
+  @unpack rhs_u          = get_rhs_variables(mesh)
+  @unpack nflx_u, bdry_u = get_bdry_variables(mesh)
 
   dg1d.interpolate_face_data!(mesh, u, bdry_u)
-  broadcast_volume!(flux_source, equation, mesh)
-  broadcast_faces!(llf_1d, equation, mesh)
-  # broadcast_bdry!(bdryllf_1d, equation, P.bdrycond, mesh)
+  broadcast_volume!(flux_source, P.equation, mesh)
+  broadcast_faces!(llf_1d, P.equation, mesh)
 
   compute_rhs_weak_form!(rhs_u, flx_u, src_u, nflx_u, mesh)
+  return
+end
+
+
+function modal_rhs!(env, mesh::Mesh1d, P::Project, hrsc::Nothing)
+  @unpack flx_u, src_u,
+          u_modal, flx_u_modal,
+          src_u_modal    = get_static_variables(mesh)
+  @unpack u              = get_dynamic_variables(mesh)
+  @unpack rhs_u          = get_rhs_variables(mesh)
+  @unpack nflx_u, bdry_u = get_bdry_variables(mesh)
+
+  u_modal .= u
+  for (v_u, v_u_modal) in zip(eachcell(mesh,u),eachcell(mesh,u_modal))
+    mul!(v_u, P.prms.V_bspline, v_u_modal)
+  end
+
+  dg1d.interpolate_face_data!(mesh, u, bdry_u)
+  broadcast_volume!(flux_source, P.equation, mesh)
+  broadcast_faces!(llf_1d, P.equation, mesh)
+
+  for (v_flx_u, v_flx_u_modal) in zip(eachcell(mesh,flx_u),eachcell(mesh,flx_u_modal))
+    mul!(v_flx_u_modal, P.prms.invV_bspline, v_flx_u)
+  end
+  for (v_src_u, v_src_u_modal) in zip(eachcell(mesh,src_u),eachcell(mesh,src_u_modal))
+    mul!(v_src_u_modal, P.prms.invV_bspline, v_src_u)
+  end
+  compute_rhs_weak_form!(rhs_u, flx_u_modal, src_u_modal, nflx_u, mesh)
+  u .= u_modal
 
   return
 end
diff --git a/src/ScalarEq/setup.jl b/src/ScalarEq/setup.jl
index 690f9b41..7e85208e 100644
--- a/src/ScalarEq/setup.jl
+++ b/src/ScalarEq/setup.jl
@@ -14,10 +14,16 @@ function Project(env::Environment, mesh::Mesh1d, prms)
   analyze_error = prms["ScalarEq"]["analyze_error"]
   analyze_error_norm = prms["ScalarEq"]["analyze_error_norm"]
   V_bernstein = dg1d.Bernstein.vandermonde_matrix(mesh.element.z)
+  if mesh.element isa DGElement && mesh.element.kind === :modal_bspline2
+    V_bspline = dg1d.Bspline.vandermonde_matrix(mesh.element.z, mesh.element.bs)
+    invV_bspline = pinv(V_bspline)
+  else
+    V_bspline, invV_bspline = nothing, nothing
+  end
   fixedprms = (; bernstein, av_derivative_scheme, av_drag, hrsc, muscl_omega,
                  slope_limiter_method, slope_limiter_tvb_M,
                  av_recompute_substeps,
-                 V_bernstein,
+                 V_bernstein, V_bspline, invV_bspline,
                  analyze_error, analyze_error_norm)
 
   # construct Project
@@ -126,6 +132,9 @@ function register_equation!(mesh::Mesh1d, P::Project)
       TODO(P.prms.hrsc)
     end
   end
+  if mesh.element isa DGElement && mesh.element.kind === :modal_bspline2
+    register_variables!(mesh.cache, static_variablenames=(:u_modal,:flx_u_modal,:src_u_modal))
+  end
 end
 function register_equation!(mesh::Mesh2d, P::Project)
   register_variables!(mesh.cache,
diff --git a/src/bspline.jl b/src/bspline.jl
index 2ac90140..281336dc 100644
--- a/src/bspline.jl
+++ b/src/bspline.jl
@@ -108,12 +108,13 @@ end
 function unsafe_interpolate(x::Real, coeffs::AbstractVector, bs::Bspline2)
   @unpack Npts, xs = bs
   @inbounds xl, xr = xs[1], xs[end]
-  xl ≤ x ≤ xr || return 0.0
+  xl == x && return coeffs[1]
+  xr == x && return coeffs[end]
+  xl < x < xr || return 0.0
   o = 2 # offset duplicated bdry knots
   v_xs = view(xs, o .+ (1:Npts))
   ir = searchsortedfirst(v_xs, x)
   il = ir-1
-  il < 1 && return coeffs[1] # x == xl
   is_supp = max(il-1,1):min(ir+1,Npts+1)
   B = 0.0
   @inbounds for i in is_supp
diff --git a/test/IntegrationTests/refs/modal_bspline2_advection_sine/modal_bspline2_advection_sine.toml b/test/IntegrationTests/refs/modal_bspline2_advection_sine/modal_bspline2_advection_sine.toml
new file mode 100644
index 00000000..3d670bb7
--- /dev/null
+++ b/test/IntegrationTests/refs/modal_bspline2_advection_sine/modal_bspline2_advection_sine.toml
@@ -0,0 +1,21 @@
+[Evolution]
+cfl = 0.5
+tend = 2.2
+
+[ScalarEq]
+analyze_error = true
+equation = "advection"
+id = "sine"
+
+[Output]
+substep_every_iteration = 200
+substep_variables = ["u", "u_err"]
+aligned_ts = "$(collect(range(0.1,2.2,step=0.1)))"
+variables1d = ["u", "u_err"]
+
+[Mesh]
+dg_kind = "modal_bspline2"
+range = [0.0, 1.0]
+k = 30
+basis = "lgl"
+n = 5
diff --git a/test/IntegrationTests/refs/modal_bspline2_advection_sine/output1d.h5 b/test/IntegrationTests/refs/modal_bspline2_advection_sine/output1d.h5
new file mode 100644
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diff --git a/test/IntegrationTests/refs/modal_bspline2_advection_sine/substep_output.h5 b/test/IntegrationTests/refs/modal_bspline2_advection_sine/substep_output.h5
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literal 0
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diff --git a/test/IntegrationTests/refs/testconfig.toml b/test/IntegrationTests/refs/testconfig.toml
index b5cdbccf..f9687bb2 100644
--- a/test/IntegrationTests/refs/testconfig.toml
+++ b/test/IntegrationTests/refs/testconfig.toml
@@ -10,6 +10,9 @@ variables1d = [ "u", "u_err" ]
 [modal_bernstein_advection_sine]
 variables1d = [ "u" ]
 
+[modal_bspline2_advection_sine]
+variables1d = [ "u", "u_err" ]
+
 [advection_sine_analysis]
 variables0d = [ "u_err_norm", "u_norm2" ]
 variables1d = [ "u" ]
-- 
GitLab