Fix redundant type conversion in LobattoLegendreBasis (#2239)

* Fix

* Fix

* Fix

* Update src/solvers/dgsem/basis_lobatto_legendre.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* Update src/solvers/dgsem/basis_lobatto_legendre.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* Update src/solvers/dgsem/basis_lobatto_legendre.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* Format

---------

Co-authored-by: Hendrik Ranocha <[email protected]>

Author: huiyuxie

src/solvers/dgsem/basis_lobatto_legendre.jl

@@ -40,31 +40,27 @@ function LobattoLegendreBasis(RealT, polydeg::Integer)
     nodes_, weights_ = gauss_lobatto_nodes_weights(nnodes_, RealT)
     inverse_weights_ = inv.(weights_)
 
-    _, inverse_vandermonde_legendre_ = vandermonde_legendre(nodes_, RealT)
+    _, inverse_vandermonde_legendre = vandermonde_legendre(nodes_, RealT)
 
-    boundary_interpolation_ = zeros(RealT, nnodes_, 2)
-    boundary_interpolation_[:, 1] = calc_lhat(-one(RealT), nodes_, weights_)
-    boundary_interpolation_[:, 2] = calc_lhat(one(RealT), nodes_, weights_)
+    boundary_interpolation = zeros(RealT, nnodes_, 2)
+    boundary_interpolation[:, 1] = calc_lhat(-one(RealT), nodes_, weights_)
+    boundary_interpolation[:, 2] = calc_lhat(one(RealT), nodes_, weights_)
 
-    derivative_matrix_ = polynomial_derivative_matrix(nodes_)
-    derivative_split_ = calc_dsplit(nodes_, weights_)
-    derivative_split_transpose_ = Matrix(derivative_split_')
-    derivative_dhat_ = calc_dhat(nodes_, weights_)
+    derivative_matrix = polynomial_derivative_matrix(nodes_)
+    derivative_split = calc_dsplit(nodes_, weights_)
+    derivative_split_transpose = Matrix(derivative_split')
+    derivative_dhat = calc_dhat(nodes_, weights_)
 
-    # type conversions to get the requested real type and enable possible
-    # optimizations of runtime performance and latency
+    # Type conversions to enable possible optimizations of runtime performance 
+    # and latency
     nodes = SVector{nnodes_, RealT}(nodes_)
     weights = SVector{nnodes_, RealT}(weights_)
     inverse_weights = SVector{nnodes_, RealT}(inverse_weights_)
 
-    inverse_vandermonde_legendre = convert.(RealT, inverse_vandermonde_legendre_)
-    boundary_interpolation = convert.(RealT, boundary_interpolation_)
-
-    # Usually as fast as `SMatrix` (when using `let` in the volume integral/`@threaded`)
-    derivative_matrix = Matrix{RealT}(derivative_matrix_)
-    derivative_split = Matrix{RealT}(derivative_split_)
-    derivative_split_transpose = Matrix{RealT}(derivative_split_transpose_)
-    derivative_dhat = Matrix{RealT}(derivative_dhat_)
+    # We keep the matrices above stored using the standard `Matrix` type 
+    # since this is usually as fast as `SMatrix`
+    # (when using `let` in the volume integral/`@threaded`)
+    # and reduces latency
 
     return LobattoLegendreBasis{RealT, nnodes_, typeof(nodes),
                                 typeof(inverse_vandermonde_legendre),