small improvements in doc

Author: chmerdon

docs/src/solvers.md

@@ -15,7 +15,7 @@ advance.
 
 !!! note
 
-    Currently it is not possible to used different finite element spaces for different multi-indices,
+    Currently it is not possible to use different finite element spaces for different multi-indices,
     but this feature might be added in the future.
 
 ```@autodocs

docs/src/tonbasis.md

@@ -2,12 +2,15 @@
 
 Each multi-index ``\mu = [\mu_1,\mu_2,\ldots,\mu_M]``
 encodes a tensorized basis function for the parameter space
-of the form ``H_\mu = \pro_{k=1}^M H_k`` where the
+of the form ``H_\mu = \prod_{k=1}^M H_k`` where the
 ``H_k`` are the orthogonal polynomials.
 The TensorizedBasis collects all information necessary
 to evaluate those basis functions, i.e. the set of multi-indices
 and the triple products of the form ``(y_mH_\mu, H_\lambda)``
-for each ``m`` and ``\mu, \lambda`` in the set of multi-indices.
+for each ``m`` and ``\mu, \lambda`` in the set of multi-indices
+as a sparse matrix. There are analytic formulas to evaluate
+these triple products in terms of recurrence coefficients, but it makes
+sense to store them for faster evaluation times.
 
 
 

docs/src/tonbasis.pdf

@@ -3,8 +3,7 @@ $(TYPEDEF)
 
 A stochastic coefficient is assumed to have the Karhunen-Loeve expansion form
 
-    ``a(x,y) = a_0(x) + ∑_m y_m a_m(x)``
-
+``a(y,x) = a_0(x) + \\sum_{m=1}^\\infty y_m a_m(x)``
 with (centered independent) random variables ``y_m`` and
 basis functions ``a_m(x)`` that need to be specified (together with their gradients)
 and expectation value ``a_0``

src/coefficients/coefficients.jl

@@ -42,7 +42,7 @@ computes the residual-based a posteriori error estimator for the current solutio
 for the given model problem and stochastic coefficient `C` and returns:
 - `eta4modes` = array with total error estimators for each multi-index (corresponding to the enriched set of multi-indices with the current active modes coming first)
 - `eta4cell` = array with total error estimators for each cell in grid (for spatial refinement)
-- `multi_indices_extended = enriched set of multi-indices used for the computations
+- `multi_indices_extended` = enriched set of multi-indices used for the computations
 
 """
 function estimate(::Type{AbstractModelProblem}, sol::SGFEVector, C::AbstractStochasticCoefficient; kwargs...)

src/estimate.jl

@@ -6,12 +6,21 @@ $(TYPEDSIGNATURES)
 solves the specified model problem with the given stochastic coefficient `C` and right-hand side `rhs`
 and writes the solution into `sol`. Via this `sol` vector the spatial and stochastic discretization
 is communicated as well as initial data for the iterative solver.
+The boolean `use_iterative_solver` (default is true) determines if the iterative solver is used
+or if the full matrix is assembled and solved by a direct solver (very slow for larger systems).
+The parameters `bonus_quadorder_f` (default is 0) and `bonus_quadorder_a` (default is 2) can be used
+to increase the quadrature order in terms that involve the rhs or the stochastic coefficient, respectively.
+
 
 """
 function solve!(
         ::Type{AbstractModelProblem},
         sol::SGFEVector,                        ## target SGFEM vector
         C::AbstractStochasticCoefficient;
+        rhs = nothing,
+        use_iterative_solver = true,
+        bonus_quadorder_f = 0,
+        bonus_quadorder_a = 0,
         kwargs...
     )
     return @error "This Model problem seems to have no solver implemented!"

src/modelproblems/modelproblems.jl

@@ -41,9 +41,9 @@ $(TYPEDSIGNATURES)
 
 adds new stochastic modes:
 - for each existing mode all neighbouring modes are added (= all possible copies of that mode where one dimension is increased by 1)
-- `p_extension' additionally ensures that the polynomial degree of the first dimension is increased by this amount
-- `tail_extension' activates tail_expansion[1] many new stochastic modes with order 1,
-   for each existing mode also the next tail_expansion[2] many higher stochastic modes are activated or increased
+- `p_extension` additionally ensures that the polynomial degree of the first dimension is increased by this amount
+- `tail_extension` activates `tail_expansion[1]` many new stochastic modes with order 1,
+   for each existing mode also the next `tail_expansion[2]` many higher stochastic modes are activated or increased
 """
 function add_boundary_modes(multi_indices; p_extension = 1, tail_extension = [10, 2])
     last_nonzero = 0 # = support

src/mopcontrol.jl

@@ -54,11 +54,13 @@ $(TYPEDSIGNATURES)
 estimates the error for the model problem `problem` by Monte carlo sampling: for each sample a discrete
 finite element solution of the deterministic model problem with fixed (sampled) coefficient with
 polynomial order `order` is computed and compared to the given stochastic Galerkin solution
-`SolutionSGFEM`. Return values are:
-- totalerrorL2stress_weighted : mean L2 error of the stress with samples weighted by the distribution
-- totalerrorL2u_weighted : mean L2 error with samples weighted by the distribution
-- totalerrorL2stress_uniform : mean L2 error of the stress with samples weighted uniformly
-- totalerrorL2u_uniform : mean L2 error with samples weighted uniformly
+`SolutionSGFEM`. Return values (each arrays of length M+1 where M is the length of the multi-indices) are:
+- `totalerrorL2stress_weighted` : mean L2 error of the stress with samples weighted by the distribution
+- `totalerrorL2u_weighted` : mean L2 error with samples weighted by the distribution
+- `totalerrorL2stress_uniform` : mean L2 error of the stress with samples weighted uniformly
+- `totalerrorL2u_uniform` : mean L2 error with samples weighted uniformly
+The m-th component of these arrays are the errors when only multi-indices of up to order m
+are included.
 
 """
 function calculate_sampling_error(