diff --git a/benches/assembly_benchmark.rs b/benches/assembly_benchmark.rs
index 32b2bc3d..8a020f4f 100644
--- a/benches/assembly_benchmark.rs
+++ b/benches/assembly_benchmark.rs
@@ -1,6 +1,6 @@
 use bempp::boundary_assemblers::BoundaryAssemblerOptions;
-use bempp::function::DefaultFunctionSpace;
 use bempp::function::FunctionSpace;
+use bempp::function::FunctionSpaceTrait;
 use bempp::laplace::assembler::single_layer;
 use criterion::{black_box, criterion_group, criterion_main, Criterion};
 use mpi;
@@ -18,7 +18,7 @@ pub fn assembly_parts_benchmark(c: &mut Criterion) {
         let grid = bempp::shapes::regular_sphere(i, 1, &comm);
         let element = LagrangeElementFamily::<f64>::new(0, Continuity::Discontinuous);
 
-        let space = DefaultFunctionSpace::new(&grid, &element);
+        let space = FunctionSpace::new(&grid, &element);
         let mut options = BoundaryAssemblerOptions::default();
         options.set_regular_quadrature_degree(ReferenceCellType::Triangle, 16);
         options.set_singular_quadrature_degree(
diff --git a/examples/assembly.rs b/examples/assembly.rs
index e9cc6f48..bfc46d40 100644
--- a/examples/assembly.rs
+++ b/examples/assembly.rs
@@ -1,5 +1,5 @@
 use bempp::boundary_assemblers::BoundaryAssemblerOptions;
-use bempp::function::DefaultFunctionSpace;
+use bempp::function::FunctionSpace;
 use bempp::laplace::assembler::single_layer;
 use ndelement::ciarlet::LagrangeElementFamily;
 use ndelement::types::{Continuity, ReferenceCellType};
@@ -11,7 +11,7 @@ fn main() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(1, Continuity::Standard);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
 
     // Adjust the quadrature degree for non-singular integrals on a triangle.
     // This makes the integrals use a quadrature rule with 16 points
diff --git a/src/boundary_assemblers.rs b/src/boundary_assemblers.rs
index eed9cad8..854088ca 100644
--- a/src/boundary_assemblers.rs
+++ b/src/boundary_assemblers.rs
@@ -8,7 +8,7 @@ use crate::boundary_assemblers::cell_pair_assemblers::{
 };
 use crate::boundary_assemblers::helpers::KernelEvaluator;
 use crate::boundary_assemblers::helpers::{equal_grids, RawData2D, RlstArray, SparseMatrixData};
-use crate::function::FunctionSpace;
+use crate::function::FunctionSpaceTrait;
 use bempp_quadrature::duffy::{
     quadrilateral_duffy, quadrilateral_triangle_duffy, triangle_duffy, triangle_quadrilateral_duffy,
 };
@@ -119,7 +119,7 @@ impl<'o, T: RlstScalar + MatrixInverse, Integrand: BoundaryIntegrand<T = T>, K:
     BoundaryAssembler<'o, T, Integrand, K>
 {
     /// Assemble the singular part into a CSR matrix.
-    pub fn assemble_singular<Space: FunctionSpace<T = T> + Sync>(
+    pub fn assemble_singular<Space: FunctionSpaceTrait<T = T> + Sync>(
         &self,
         trial_space: &Space,
         test_space: &Space,
@@ -155,7 +155,7 @@ impl<'o, T: RlstScalar + MatrixInverse, Integrand: BoundaryIntegrand<T = T>, K:
     }
 
     /// Assemble into a dense matrix.
-    pub fn assemble<Space: FunctionSpace<T = T> + Sync>(
+    pub fn assemble<Space: FunctionSpaceTrait<T = T> + Sync>(
         &self,
         trial_space: &Space,
         test_space: &Space,
@@ -173,7 +173,7 @@ impl<'o, T: RlstScalar + MatrixInverse, Integrand: BoundaryIntegrand<T = T>, K:
     }
 
     /// Assemble into a dense matrix.
-    pub fn assemble_into_memory<Space: FunctionSpace<T = T> + Sync>(
+    pub fn assemble_into_memory<Space: FunctionSpaceTrait<T = T> + Sync>(
         &self,
         trial_space: &Space,
         test_space: &Space,
@@ -231,7 +231,7 @@ impl<'o, T: RlstScalar + MatrixInverse, Integrand: BoundaryIntegrand<T = T>, K:
     }
 
     /// Assemble the singular contributions
-    fn assemble_singular_part<Space: FunctionSpace<T = T> + Sync>(
+    fn assemble_singular_part<Space: FunctionSpaceTrait<T = T> + Sync>(
         &self,
         shape: [usize; 2],
         trial_space: &Space,
@@ -393,7 +393,7 @@ impl<'o, T: RlstScalar + MatrixInverse, Integrand: BoundaryIntegrand<T = T>, K:
     }
 
     /// Assemble the non-singular contributions into a dense matrix
-    fn assemble_nonsingular_part<Space: FunctionSpace<T = T> + Sync>(
+    fn assemble_nonsingular_part<Space: FunctionSpaceTrait<T = T> + Sync>(
         &self,
         output: &RawData2D<T>,
         trial_space: &Space,
@@ -609,7 +609,7 @@ where
 #[allow(clippy::too_many_arguments)]
 fn assemble_batch_singular<
     T: RlstScalar + MatrixInverse,
-    Space: FunctionSpace<T = T>,
+    Space: FunctionSpaceTrait<T = T>,
     Integrand: BoundaryIntegrand<T = T>,
     K: Kernel<T = T>,
 >(
@@ -688,7 +688,7 @@ fn assemble_batch_singular<
 #[allow(clippy::too_many_arguments)]
 fn assemble_batch_nonadjacent<
     T: RlstScalar + MatrixInverse,
-    Space: FunctionSpace<T = T>,
+    Space: FunctionSpaceTrait<T = T>,
     Integrand: BoundaryIntegrand<T = T>,
     K: Kernel<T = T>,
 >(
diff --git a/src/function.rs b/src/function.rs
index a4480caa..c725505a 100644
--- a/src/function.rs
+++ b/src/function.rs
@@ -18,7 +18,7 @@ type DofList = Vec<Vec<usize>>;
 type OwnerData = Vec<(usize, usize, usize, usize)>;
 
 /// A function space
-pub trait FunctionSpace {
+pub trait FunctionSpaceTrait {
     /// Communicator
     type C: Communicator;
     /// Scalar type
@@ -70,7 +70,7 @@ pub trait FunctionSpace {
 }
 
 /// Implementation of a general function space.
-pub struct DefaultFunctionSpace<
+pub struct FunctionSpace<
     'a,
     C: Communicator,
     T: RlstScalar + MatrixInverse,
@@ -88,11 +88,10 @@ pub struct DefaultFunctionSpace<
 }
 
 unsafe impl<
-        'a,
         C: Communicator,
         T: RlstScalar + MatrixInverse,
         GridImpl: ParallelGrid<C> + Grid<T = T::Real, EntityDescriptor = ReferenceCellType>,
-    > Sync for DefaultFunctionSpace<'a, C, T, GridImpl>
+    > Sync for FunctionSpace<'_, C, T, GridImpl>
 {
 }
 
@@ -101,7 +100,7 @@ impl<
         C: Communicator,
         T: RlstScalar + MatrixInverse,
         GridImpl: ParallelGrid<C> + Grid<T = T::Real, EntityDescriptor = ReferenceCellType>,
-    > DefaultFunctionSpace<'a, C, T, GridImpl>
+    > FunctionSpace<'a, C, T, GridImpl>
 {
     /// Create new function space
     pub fn new(
@@ -239,11 +238,10 @@ impl<
 }
 
 impl<
-        'a,
         C: Communicator,
         T: RlstScalar + MatrixInverse,
         GridImpl: ParallelGrid<C> + Grid<T = T::Real, EntityDescriptor = ReferenceCellType>,
-    > FunctionSpace for DefaultFunctionSpace<'a, C, T, GridImpl>
+    > FunctionSpaceTrait for FunctionSpace<'_, C, T, GridImpl>
 {
     type T = T;
     type Grid = GridImpl;
diff --git a/tests/compare_to_bempp_cl.rs b/tests/compare_to_bempp_cl.rs
index ab17626f..a1ceb527 100644
--- a/tests/compare_to_bempp_cl.rs
+++ b/tests/compare_to_bempp_cl.rs
@@ -2,7 +2,7 @@ use std::sync::LazyLock;
 
 use approx::*;
 use bempp::boundary_assemblers::BoundaryAssemblerOptions;
-use bempp::function::DefaultFunctionSpace;
+use bempp::function::FunctionSpace;
 use bempp::{helmholtz, laplace};
 use cauchy::c64;
 use mpi::environment::Universe;
@@ -23,7 +23,7 @@ fn test_laplace_single_layer_dp0_dp0() {
 
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = laplace::assembler::single_layer(&options).assemble(&space, &space);
@@ -45,7 +45,7 @@ fn test_laplace_double_layer_dp0_dp0() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = laplace::assembler::double_layer(&options).assemble(&space, &space);
@@ -67,7 +67,7 @@ fn test_laplace_adjoint_double_layer_dp0_dp0() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = laplace::assembler::adjoint_double_layer(&options).assemble(&space, &space);
@@ -90,7 +90,7 @@ fn test_laplace_hypersingular_p1_p1() {
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
 
     let element = LagrangeElementFamily::<f64>::new(1, Continuity::Standard);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = laplace::assembler::hypersingular(&options).assemble(&space, &space);
@@ -118,7 +118,7 @@ fn test_helmholtz_single_layer_dp0_dp0() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<c64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = helmholtz::assembler::single_layer(3.0, &options).assemble(&space, &space);
@@ -140,7 +140,7 @@ fn test_helmholtz_double_layer_dp0_dp0() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<c64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = helmholtz::assembler::double_layer(3.0, &options).assemble(&space, &space);
@@ -161,7 +161,7 @@ fn test_helmholtz_adjoint_double_layer_dp0_dp0() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<c64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = helmholtz::assembler::adjoint_double_layer(3.0, &options).assemble(&space, &space);
@@ -183,7 +183,7 @@ fn test_helmholtz_hypersingular_p1_p1() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = bempp::shapes::regular_sphere(0, 1, &comm);
     let element = LagrangeElementFamily::<c64>::new(1, Continuity::Standard);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let options = BoundaryAssemblerOptions::default();
 
     let matrix = helmholtz::assembler::hypersingular(3.0, &options).assemble(&space, &space);
diff --git a/tests/test_space.rs b/tests/test_space.rs
index 531b0970..6d1d9e78 100644
--- a/tests/test_space.rs
+++ b/tests/test_space.rs
@@ -1,6 +1,5 @@
-use bempp::function::{assign_dofs, DefaultFunctionSpace, FunctionSpace};
+use bempp::function::{assign_dofs, FunctionSpace, FunctionSpaceTrait};
 use bempp::shapes::{regular_sphere, screen_triangles};
-use mpi::topology::SimpleCommunicator;
 use ndelement::ciarlet::{LagrangeElementFamily, RaviartThomasElementFamily};
 use ndelement::types::{Continuity, ReferenceCellType};
 use ndgrid::traits::{Entity, Grid, Topology};
@@ -14,13 +13,6 @@ static MPI_UNIVERSE: LazyLock<Universe> = std::sync::LazyLock::new(|| {
         .0
 });
 
-fn get_comm() -> SimpleCommunicator {
-    use mpi;
-
-    let _ = mpi::initialize();
-    mpi::topology::SimpleCommunicator::self_comm()
-}
-
 fn run_test(
     grid: &(impl Grid<T = f64, EntityDescriptor = ReferenceCellType> + Sync),
     degree: usize,
@@ -149,7 +141,7 @@ fn test_dofmap_lagrange0() {
     let grid = regular_sphere::<f64, _>(2, 1, &comm);
     //let grid = regular_sphere::<f64, _>(2, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     assert_eq!(space.local_size(), space.global_size());
     assert_eq!(
         space.local_size(),
@@ -163,7 +155,7 @@ fn test_dofmap_lagrange1() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = regular_sphere::<f64, _>(2, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(1, Continuity::Standard);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     assert_eq!(space.local_size(), space.global_size());
     assert_eq!(
         space.local_size(),
@@ -177,7 +169,7 @@ fn test_dofmap_lagrange2() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = regular_sphere::<f64, _>(2, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(2, Continuity::Standard);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     assert_eq!(space.local_size(), space.global_size());
     assert_eq!(
         space.local_size(),
@@ -192,7 +184,7 @@ fn test_colouring_p1() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = regular_sphere::<f64, _>(2, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(1, Continuity::Standard);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let colouring = &space.cell_colouring()[&ReferenceCellType::Triangle];
     let cells = grid.entity_iter(2).collect::<Vec<_>>();
     let mut n = 0;
@@ -232,7 +224,7 @@ fn test_colouring_dp0() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = regular_sphere::<f64, _>(2, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(0, Continuity::Discontinuous);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let colouring = &space.cell_colouring()[&ReferenceCellType::Triangle];
     let mut n = 0;
     for i in colouring {
@@ -259,7 +251,7 @@ fn test_colouring_rt1() {
     let comm = mpi::topology::SimpleCommunicator::self_comm();
     let grid = regular_sphere::<f64, _>(2, 1, &comm);
     let element = LagrangeElementFamily::<f64>::new(1, Continuity::Standard);
-    let space = DefaultFunctionSpace::new(&grid, &element);
+    let space = FunctionSpace::new(&grid, &element);
     let colouring = &space.cell_colouring()[&ReferenceCellType::Triangle];
     let mut n = 0;
     for i in colouring {