diff --git a/.basedpyright/baseline.json b/.basedpyright/baseline.json
index 4cf269371..fa3f4c231 100644
--- a/.basedpyright/baseline.json
+++ b/.basedpyright/baseline.json
@@ -778,11 +778,11 @@
                 }
             },
             {
-                "code": "reportIndexIssue",
+                "code": "reportUnreachable",
                 "range": {
-                    "startColumn": 12,
-                    "endColumn": 17,
-                    "lineCount": 1
+                    "startColumn": 8,
+                    "endColumn": 45,
+                    "lineCount": 7
                 }
             },
             {
@@ -908,11 +908,11 @@
                 }
             },
             {
-                "code": "reportIndexIssue",
+                "code": "reportUnreachable",
                 "range": {
-                    "startColumn": 12,
-                    "endColumn": 17,
-                    "lineCount": 1
+                    "startColumn": 8,
+                    "endColumn": 45,
+                    "lineCount": 7
                 }
             },
             {
@@ -924,43 +924,11 @@
                 }
             },
             {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 19,
-                    "endColumn": 41,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownVariableType",
-                "range": {
-                    "startColumn": 32,
-                    "endColumn": 44,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownMemberType",
+                "code": "reportUnreachable",
                 "range": {
                     "startColumn": 8,
                     "endColumn": 17,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 8,
-                    "endColumn": 19,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 8,
-                    "endColumn": 15,
-                    "lineCount": 1
+                    "lineCount": 8
                 }
             }
         ],
@@ -21186,35 +21154,11 @@
                 }
             },
             {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 28,
-                    "endColumn": 33,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 46,
-                    "endColumn": 63,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 46,
-                    "endColumn": 63,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportArgumentType",
+                "code": "reportUnreachable",
                 "range": {
-                    "startColumn": 41,
-                    "endColumn": 53,
-                    "lineCount": 1
+                    "startColumn": 8,
+                    "endColumn": 56,
+                    "lineCount": 4
                 }
             },
             {
@@ -28689,6 +28633,14 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportAbstractUsage",
+                "range": {
+                    "startColumn": 19,
+                    "endColumn": 18,
+                    "lineCount": 4
+                }
+            },
             {
                 "code": "reportCallIssue",
                 "range": {
@@ -28817,6 +28769,14 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportAbstractUsage",
+                "range": {
+                    "startColumn": 19,
+                    "endColumn": 18,
+                    "lineCount": 4
+                }
+            },
             {
                 "code": "reportCallIssue",
                 "range": {
@@ -44037,14 +43997,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportUnnecessaryTypeIgnoreComment",
-                "range": {
-                    "startColumn": 97,
-                    "endColumn": 117,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnknownVariableType",
                 "range": {
@@ -44053,38 +44005,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportUnknownVariableType",
-                "range": {
-                    "startColumn": 12,
-                    "endColumn": 18,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportOptionalSubscript",
-                "range": {
-                    "startColumn": 21,
-                    "endColumn": 48,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 49,
-                    "endColumn": 70,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 49,
-                    "endColumn": 55,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnknownMemberType",
                 "range": {
@@ -44260,6 +44180,24 @@
                 }
             }
         ],
+        "./test/test_layer_pot_eigenvalues.py": [
+            {
+                "code": "reportUnreachable",
+                "range": {
+                    "startColumn": 12,
+                    "endColumn": 21,
+                    "lineCount": 8
+                }
+            },
+            {
+                "code": "reportUnreachable",
+                "range": {
+                    "startColumn": 12,
+                    "endColumn": 21,
+                    "lineCount": 4
+                }
+            }
+        ],
         "./test/test_layer_pot_identity.py": [
             {
                 "code": "reportReturnType",
diff --git a/doc/conf.py b/doc/conf.py
index 1d2b79e0e..a6a727a03 100644
--- a/doc/conf.py
+++ b/doc/conf.py
@@ -101,7 +101,7 @@
     # sumpy
     "ExpansionBase": "class:sumpy.expansion.ExpansionBase",
     "ExpansionFactoryBase": "class:sumpy.expansion.ExpansionFactoryBase",
-    "Kernel": "class:sumpy.kernel.Kernel",
+    "ScalarKernel": "class:sumpy.kernel.ScalarKernel",
     "HelmholtzKernel": "class:sumpy.kernel.HelmholtzKernel",
     "P2P": "class:sumpy.p2p.P2P",
     "P2PBase": "class:sumpy.p2p.P2PBase",
diff --git a/pytential/linalg/proxy.py b/pytential/linalg/proxy.py
index 86c0adc65..d5d47063d 100644
--- a/pytential/linalg/proxy.py
+++ b/pytential/linalg/proxy.py
@@ -51,7 +51,7 @@
 
     from boxtree.tree_build import TreeKind
     from sumpy.expansion import ExpansionBase
-    from sumpy.kernel import Kernel
+    from sumpy.kernel import ScalarKernel
 
     from pytential.linalg.utils import IndexList
     from pytential.symbolic.dof_desc import DOFDescriptorLike
@@ -182,7 +182,7 @@ def __init__(self,
         self.lpot_source = lpot_source
 
     def get_expansion_for_qbx_direct_eval(
-            self, base_kernel: Kernel, target_kernels: Sequence[Kernel]
+            self, base_kernel: ScalarKernel, target_kernels: Sequence[ScalarKernel]
         ) -> ExpansionBase:
         """Wrapper around
         ``pytential.qbx.QBXLayerPotentialSource.get_expansion_for_qbx_direct_eval``
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index e628027e8..0e704e9cc 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -58,7 +58,7 @@
     from pymbolic import ArithmeticExpression
     from sumpy.expansion import LocalExpansionFactory
     from sumpy.fmm import FMMLevelToOrder
-    from sumpy.kernel import Kernel
+    from sumpy.kernel import ScalarKernel
 
     from pytential.collection import GeometryCollection, GeometryLike
     from pytential.qbx.cost import AbstractQBXCostModel
@@ -99,7 +99,7 @@ class QBXDefaultExpansionFactory(DefaultExpansionFactoryBase):
     """An expansion factory to create QBX local, local and multipole expansions
     """
     def get_qbx_local_expansion_class(self,
-                kernel: Kernel, /
+                kernel: ScalarKernel, /
             ) -> LocalExpansionFactory:
         local_expn_class = DefaultExpansionFactoryBase.get_local_expansion_class(
                 self, kernel)
@@ -199,7 +199,7 @@ def __init__(
         :arg fmm_level_to_order: A callable that takes arguments of
             *(kernel, kernel_args, tree, level)* and returns the expansion
             order to be used on a given *level* of *tree* with *kernel*, where
-            *kernel* is the :class:`sumpy.kernel.Kernel` being evaluated, and
+            *kernel* is the :class:`sumpy.kernel.ScalarKernel` being evaluated, and
             *kernel_args* is a set of *(key, value)* tuples with evaluated
             kernel arguments. May not be given if *fmm_order* is given.
         :arg fmm_backend: a string denoting the desired FMM backend to use,
diff --git a/pytential/source.py b/pytential/source.py
index b0329dcc7..f3c254ea1 100644
--- a/pytential/source.py
+++ b/pytential/source.py
@@ -45,7 +45,7 @@
 
     import pyopencl as cl
     from meshmode.discretization import Discretization
-    from sumpy.kernel import Kernel
+    from sumpy.kernel import ScalarKernel
     from sumpy.p2p import P2P
 
     from pytential.collection import GeometryCollection
@@ -103,16 +103,16 @@ def op_group_features(self, expr: IntG) -> tuple[Hashable, ...]:
 
     def get_p2p(self,
                 actx: PyOpenCLArrayContext,
-                target_kernels: tuple[Kernel, ...],
-                source_kernels: tuple[Kernel, ...] | None = None) -> P2P:
+                target_kernels: tuple[ScalarKernel, ...],
+                source_kernels: tuple[ScalarKernel, ...] | None = None) -> P2P:
         """
         :returns: a subclass of :class:`~sumpy.p2p.P2P` for evaluating
             the *target_kernels* and the *source_kernels* on the source geometry.
         """
 
         @memoize_in(actx, (PotentialSource, "p2p"))
-        def p2p(target_kernels: tuple[Kernel, ...],
-                source_kernels: tuple[Kernel, ...] | None) -> P2P:
+        def p2p(target_kernels: tuple[ScalarKernel, ...],
+                source_kernels: tuple[ScalarKernel, ...] | None) -> P2P:
             if any(knl.is_complex_valued for knl in target_kernels):
                 value_dtype = self.complex_dtype
             else:
@@ -364,7 +364,7 @@ def complex_dtype(self) -> np.dtype[np.complexfloating]:
 
     # {{{ fmm setup helpers
 
-    def get_fmm_kernel(self, kernels: Iterable[Kernel]) -> Kernel | None:
+    def get_fmm_kernel(self, kernels: Iterable[ScalarKernel]) -> ScalarKernel | None:
         fmm_kernel = None
 
         from sumpy.kernel import TargetTransformationRemover
@@ -380,7 +380,7 @@ def get_fmm_kernel(self, kernels: Iterable[Kernel]) -> Kernel | None:
 
     def get_fmm_output_and_expansion_dtype(
             self,
-            kernels: Iterable[Kernel],
+            kernels: Iterable[ScalarKernel],
             strengths: ArrayOrContainerOrScalar) -> np.dtype[Any]:
         if (
                 any(knl.is_complex_valued for knl in kernels)
@@ -392,7 +392,7 @@ def get_fmm_output_and_expansion_dtype(
     def get_fmm_expansion_wrangler_extra_kwargs(
             self,
             actx: PyOpenCLArrayContext,
-            target_kernels: tuple[Kernel, ...],
+            target_kernels: tuple[ScalarKernel, ...],
             tree_user_source_ids: Array,
             arguments: KernelArgumentMapping,
             evaluator: Callable[[Operand], ArrayOrContainerOrScalar],
diff --git a/pytential/symbolic/compiler.py b/pytential/symbolic/compiler.py
index ae8e12b06..e17a2589f 100644
--- a/pytential/symbolic/compiler.py
+++ b/pytential/symbolic/compiler.py
@@ -54,7 +54,7 @@
     from pymbolic.geometric_algebra import MultiVector
     from pymbolic.mapper.dependency import Dependency
     from pymbolic.typing import Expression
-    from sumpy.kernel import Kernel
+    from sumpy.kernel import ScalarKernel
 
     from pytential.collection import GeometryCollection
     from pytential.symbolic.primitives import KernelArgumentMapping, Operand
@@ -229,14 +229,14 @@ class ComputePotential(Statement):
     """A tuple of :class:`PotentialOutput` instances. The entries in the list
     correspond to :attr:`Statement.names`.
     """
-    target_kernels: tuple[Kernel, ...]
-    """A tuple of :class:`sumpy.kernel.Kernel` instances, indexed by
+    target_kernels: tuple[ScalarKernel, ...]
+    """A tuple of :class:`sumpy.kernel.ScalarKernel` instances, indexed by
     :attr:`PotentialOutput.target_kernel_index`.
     """
     kernel_arguments: KernelArgumentMapping
     """A dictionary mapping argument names to kernel arguments."""
-    source_kernels: tuple[Kernel, ...]
-    """A tuple of :class:`sumpy.kernel.Kernel` instances with only source
+    source_kernels: tuple[ScalarKernel, ...]
+    """A tuple of :class:`sumpy.kernel.ScalarKernel` instances with only source
     derivatives and no target derivatives. See the
     :class:`~pytential.symbolic.primitives.IntG` docstring for details.
     """
diff --git a/pytential/symbolic/pde/beltrami.py b/pytential/symbolic/pde/beltrami.py
index b1e7fdee7..d6b515b7f 100644
--- a/pytential/symbolic/pde/beltrami.py
+++ b/pytential/symbolic/pde/beltrami.py
@@ -39,7 +39,7 @@
 
 
 if TYPE_CHECKING:
-    from sumpy.kernel import Kernel
+    from sumpy.kernel import ScalarKernel
 
 
 # {{{ beltrami operator
@@ -85,7 +85,8 @@ class BeltramiOperator:
     .. automethod:: operator
     """
 
-    def __init__(self, kernel: Kernel, *,
+    def __init__(
+            self, kernel: ScalarKernel, *,
             dim: int | None = None,
             precond: str = "left",
             kernel_arguments: dict[str, Any] | None = None) -> None:
diff --git a/pytential/symbolic/pde/scalar.py b/pytential/symbolic/pde/scalar.py
index 48dc71584..2f3ab96f5 100644
--- a/pytential/symbolic/pde/scalar.py
+++ b/pytential/symbolic/pde/scalar.py
@@ -44,7 +44,7 @@
 from typing_extensions import override
 
 from pymbolic.typing import ArithmeticExpression
-from sumpy.kernel import DirectionalSourceDerivative, Kernel
+from sumpy.kernel import DirectionalSourceDerivative, ScalarKernel
 
 from pytential import sym
 
@@ -96,14 +96,14 @@ class L2WeightedPDEOperator(ABC):
     .. automethod:: __init__
     """
 
-    kernel: Kernel
+    kernel: ScalarKernel
     """The kernel used in the integral operator."""
     use_l2_weighting: bool
     """If *True*, :math:`L^2`-weighting is performed. This can be turned off for
     testing purposes, but should be enabled for other applications.
     """
 
-    def __init__(self, kernel: Kernel, *, use_l2_weighting: bool = True) -> None:
+    def __init__(self, kernel: ScalarKernel, *, use_l2_weighting: bool = True) -> None:
         self.kernel = kernel
         self.use_l2_weighting = use_l2_weighting
 
@@ -237,13 +237,13 @@ class DirichletOperator(L2WeightedPDEOperator):
 
     def __init__(
             self,
-            kernel: Kernel,
+            kernel: ScalarKernel,
             loc_sign: Side, *,
             alpha: complex | None = None,
             use_l2_weighting: bool = False,
             kernel_arguments: dict[str, Operand] | None = None) -> None:
         assert loc_sign in [-1, 1]
-        assert isinstance(kernel, Kernel)
+        assert isinstance(kernel, ScalarKernel)
 
         if kernel_arguments is None:
             kernel_arguments = {}
@@ -398,14 +398,14 @@ class NeumannOperator(L2WeightedPDEOperator):
     """
 
     def __init__(self,
-            kernel: Kernel,
+            kernel: ScalarKernel,
             loc_sign: Side, *,
             alpha: complex | None = None,
             use_improved_operator: bool = True,
             use_l2_weighting: bool = False,
             kernel_arguments: dict[str, Any] | None = None):
         assert loc_sign in [-1, 1]
-        assert isinstance(kernel, Kernel)
+        assert isinstance(kernel, ScalarKernel)
 
         if kernel_arguments is None:
             kernel_arguments = {}
@@ -589,12 +589,12 @@ class BiharmonicClampedPlateOperator:
     .. automethod:: __init__
     """
 
-    kernel: Kernel
+    kernel: ScalarKernel
     """The kernel used in the integral operator."""
     loc_sign: Side
     """Side of the operator evaluation."""
 
-    def __init__(self, kernel: Kernel, loc_sign: Side) -> None:
+    def __init__(self, kernel: ScalarKernel, loc_sign: Side) -> None:
         if loc_sign != -1:
             raise ValueError(
                 "only interior problems (loc_sign == -1) are supported")
@@ -644,10 +644,10 @@ def default_map_potentials(x: ArithmeticExpression) -> ArithmeticExpression:
 
             map_potentials = default_map_potentials
 
-        def dn(knl: Kernel) -> Kernel:
+        def dn(knl: ScalarKernel) -> ScalarKernel:
             return DirectionalSourceDerivative(knl, "normal_dir")
 
-        def dt(knl: Kernel) -> Kernel:
+        def dt(knl: ScalarKernel) -> ScalarKernel:
             return DirectionalSourceDerivative(knl, "tangent_dir")
 
         from pytools.obj_array import from_numpy
diff --git a/pytential/symbolic/primitives.py b/pytential/symbolic/primitives.py
index ccc4ec2d4..b46006510 100644
--- a/pytential/symbolic/primitives.py
+++ b/pytential/symbolic/primitives.py
@@ -67,7 +67,7 @@
     ShapeT,
     from_numpy,
 )
-from sumpy.kernel import Kernel
+from sumpy.kernel import ScalarKernel
 from sumpy.symbolic import SpatialConstant
 
 from pytential.symbolic.dof_desc import (
@@ -1871,8 +1871,8 @@ class IntG(ExpressionNode):
     .. autoattribute:: kernel_arguments
     """
 
-    target_kernel: Kernel
-    """An instance of :class:`~sumpy.kernel.Kernel` with only target dervatives
+    target_kernel: ScalarKernel
+    """An instance of :class:`~sumpy.kernel.ScalarKernel` with only target dervatives
     attached. This represents the target derivative operator :math:`T` above.
 
     Note that the term ``target_kernel`` is bad as it's not a kernel and merely
@@ -1880,8 +1880,8 @@ class IntG(ExpressionNode):
     properly supports derivative operators. This also means that the user has to
     make sure that base kernels of all the kernels passed are the same.
     """
-    source_kernels: tuple[Kernel, ...]
-    """A tuple of instances of :class:`~sumpy.kernel.Kernel` with only source
+    source_kernels: tuple[ScalarKernel, ...]
+    """A tuple of instances of :class:`~sumpy.kernel.ScalarKernel` with only source
     derivatives attached. k-th elements represents the k-th source derivative
     operator above.
     """
@@ -1920,16 +1920,16 @@ class IntG(ExpressionNode):
     """
 
     kernel_arguments: KernelArgumentMapping = field(default_factory=dict)
-    """A dictionary mapping named :class:`~sumpy.kernel.Kernel` arguments
-    (see :meth:`~sumpy.kernel.Kernel.get_args` and
-    :meth:`~sumpy.kernel.Kernel.get_source_args`) to expressions that determine
+    """A dictionary mapping named :class:`~sumpy.kernel.ScalarKernel` arguments
+    (see :meth:`~sumpy.kernel.ScalarKernel.get_args` and
+    :meth:`~sumpy.kernel.ScalarKernel.get_source_args`) to expressions that determine
     them.
     """
 
     def __init__(
             self,
-            target_kernel: Kernel,
-            source_kernels: Iterable[Kernel],
+            target_kernel: ScalarKernel,
+            source_kernels: Iterable[ScalarKernel],
             densities: Iterable[ArithmeticExpression],
             qbx_forced_limit: QBXForcedLimit,
             source: DOFDescriptorLike | None = None,
@@ -2088,7 +2088,7 @@ def __hash__(self) -> int:
 _DIR_VEC_NAME = "dsource_vec"
 
 
-def _insert_source_derivative_into_kernel(kernel: Kernel) -> Kernel:
+def _insert_source_derivative_into_kernel(kernel: ScalarKernel) -> ScalarKernel:
     # Inserts the source derivative at the innermost kernel wrapping level.
     from sumpy.kernel import DirectionalSourceDerivative
 
@@ -2139,7 +2139,7 @@ def map_quotient(self, expr: Quotient) -> CoeffsT:
 def int_g_dsource(
             ambient_dim: int,
             dsource: MultiVector[ArithmeticExpression],
-            kernel: Kernel,
+            kernel: ScalarKernel,
             density: Operand,
             qbx_forced_limit: QBXForcedLimit,
             source: DOFDescriptorLike | None = None,
@@ -2193,7 +2193,7 @@ class _unspecified:  # noqa: N801
 
 
 def int_g_vec(
-        kernel: Kernel,
+        kernel: ScalarKernel,
         density: OperandTc,
         qbx_forced_limit: QBXForcedLimit,
         source: DOFDescriptorLike = None,
@@ -2248,7 +2248,7 @@ def make_op(operand_i: ArithmeticExpression) -> IntG:
 
 
 def S(
-        kernel: Kernel,
+        kernel: ScalarKernel,
         density: OperandTc,
         qbx_forced_limit: QBXForcedLimit = _unspecified,
         source: DOFDescriptorLike = None,
@@ -2311,7 +2311,7 @@ def normal_second_derivative(
 
 
 def Sp(
-        kernel: Kernel,
+        kernel: ScalarKernel,
         density: OperandTc,
         qbx_forced_limit: QBXForcedLimit = _unspecified,
         source: DOFDescriptorLike | None = None,
@@ -2326,7 +2326,7 @@ def Sp(
              "Choosing default 'avg'.", stacklevel=2)
         qbx_forced_limit = "avg"
 
-    if ambient_dim is None and isinstance(kernel, Kernel):
+    if ambient_dim is None and isinstance(kernel, ScalarKernel):
         ambient_dim = kernel.dim
 
     if ambient_dim is None:
@@ -2341,7 +2341,7 @@ def Sp(
 
 
 def Spp(
-        kernel: Kernel,
+        kernel: ScalarKernel,
         density: ArithmeticExpression,
         qbx_forced_limit: QBXForcedLimit = _unspecified,
         source: DOFDescriptorLike | None = None,
@@ -2356,7 +2356,7 @@ def Spp(
              "Choosing default '+1'.", stacklevel=2)
         qbx_forced_limit = +1
 
-    if ambient_dim is None and isinstance(kernel, Kernel):
+    if ambient_dim is None and isinstance(kernel, ScalarKernel):
         ambient_dim = kernel.dim
 
     if ambient_dim is None:
@@ -2371,7 +2371,7 @@ def Spp(
 
 
 def D(
-        kernel: Kernel,
+        kernel: ScalarKernel,
         density: OperandTc,
         qbx_forced_limit: QBXForcedLimit = _unspecified,
         source: DOFDescriptorLike | None = None,
@@ -2386,7 +2386,7 @@ def D(
              "Choosing default 'avg'.", stacklevel=2)
         qbx_forced_limit = "avg"
 
-    if ambient_dim is None and isinstance(kernel, Kernel):
+    if ambient_dim is None and isinstance(kernel, ScalarKernel):
         ambient_dim = kernel.dim
 
     if ambient_dim is None:
@@ -2405,7 +2405,7 @@ def D(
 
 
 def Dp(
-        kernel: Kernel,
+        kernel: ScalarKernel,
         density: OperandTc,
         qbx_forced_limit: QBXForcedLimit = _unspecified,
         source: DOFDescriptorLike | None = None,
@@ -2420,7 +2420,7 @@ def Dp(
              "Choosing default '+1'.", stacklevel=2)
         qbx_forced_limit = +1
 
-    if ambient_dim is None and isinstance(kernel, Kernel):
+    if ambient_dim is None and isinstance(kernel, ScalarKernel):
         ambient_dim = kernel.dim
 
     if ambient_dim is None:
diff --git a/pytential/symbolic/stokes.py b/pytential/symbolic/stokes.py
index 4ae4cafbc..7c7f71f11 100644
--- a/pytential/symbolic/stokes.py
+++ b/pytential/symbolic/stokes.py
@@ -25,7 +25,11 @@
 
 import numpy as np
 
-from sumpy.kernel import LaplaceKernel, StokesletKernel, StressletKernel
+from sumpy.kernel import (
+    LaplaceKernel,
+    StokesletComponentKernel,
+    StressletComponentKernel,
+)
 
 from pytential import sym
 
@@ -43,7 +47,7 @@
 # {{{ StokesletWrapper
 
 class StokesletWrapper:
-    """Wrapper class for the :class:`~sumpy.kernel.StokesletKernel` kernel.
+    """Wrapper class for the :class:`~sumpy.kernel.StokesletComponentKernel` kernel.
 
     This class is meant to shield the user from the messiness of writing
     out every term in the expansion of the double-indexed Stokeslet kernel
@@ -84,23 +88,21 @@ def __init__(self, dim: int):
 
         if dim == 2:
             self.kernel_dict = {
-                        (2, 0): StokesletKernel(dim=2, icomp=0, jcomp=0),
-                        (1, 1): StokesletKernel(dim=2, icomp=0, jcomp=1),
-                        (0, 2): StokesletKernel(dim=2, icomp=1, jcomp=1)
-                               }
-
+                (2, 0): StokesletComponentKernel(dim=2, icomp=0, jcomp=0),
+                (1, 1): StokesletComponentKernel(dim=2, icomp=0, jcomp=1),
+                (0, 2): StokesletComponentKernel(dim=2, icomp=1, jcomp=1)
+            }
         elif dim == 3:
             self.kernel_dict = {
-                        (2, 0, 0): StokesletKernel(dim=3, icomp=0, jcomp=0),
-                        (1, 1, 0): StokesletKernel(dim=3, icomp=0, jcomp=1),
-                        (1, 0, 1): StokesletKernel(dim=3, icomp=0, jcomp=2),
-                        (0, 2, 0): StokesletKernel(dim=3, icomp=1, jcomp=1),
-                        (0, 1, 1): StokesletKernel(dim=3, icomp=1, jcomp=2),
-                        (0, 0, 2): StokesletKernel(dim=3, icomp=2, jcomp=2)
-                               }
-
+                (2, 0, 0): StokesletComponentKernel(dim=3, icomp=0, jcomp=0),
+                (1, 1, 0): StokesletComponentKernel(dim=3, icomp=0, jcomp=1),
+                (1, 0, 1): StokesletComponentKernel(dim=3, icomp=0, jcomp=2),
+                (0, 2, 0): StokesletComponentKernel(dim=3, icomp=1, jcomp=1),
+                (0, 1, 1): StokesletComponentKernel(dim=3, icomp=1, jcomp=2),
+                (0, 0, 2): StokesletComponentKernel(dim=3, icomp=2, jcomp=2)
+            }
         else:
-            raise ValueError("unsupported dimension given to StokesletWrapper")
+            raise ValueError(f"unsupported dimension given to StokesletWrapper: {dim}")
 
     def apply(self, density_vec_sym, mu_sym, qbx_forced_limit):
         """Symbolic expressions for integrating Stokeslet kernel.
@@ -273,7 +275,7 @@ def apply_stress(self, density_vec_sym, dir_vec_sym,
 # {{{ StressletWrapper
 
 class StressletWrapper:
-    """Wrapper class for the :class:`~sumpy.kernel.StressletKernel` kernel.
+    """Wrapper class for the :class:`~sumpy.kernel.StressletComponentKernel` kernel.
 
     This class is meant to shield the user from the messiness of writing
     out every term in the expansion of the triple-indexed Stresslet
@@ -313,28 +315,26 @@ def __init__(self, dim: int):
 
         if dim == 2:
             self.kernel_dict = {
-                (3, 0): StressletKernel(dim=2, icomp=0, jcomp=0, kcomp=0),
-                (2, 1): StressletKernel(dim=2, icomp=0, jcomp=0, kcomp=1),
-                (1, 2): StressletKernel(dim=2, icomp=0, jcomp=1, kcomp=1),
-                (0, 3): StressletKernel(dim=2, icomp=1, jcomp=1, kcomp=1)
-                               }
-
+                (3, 0): StressletComponentKernel(dim=2, icomp=0, jcomp=0, kcomp=0),
+                (2, 1): StressletComponentKernel(dim=2, icomp=0, jcomp=0, kcomp=1),
+                (1, 2): StressletComponentKernel(dim=2, icomp=0, jcomp=1, kcomp=1),
+                (0, 3): StressletComponentKernel(dim=2, icomp=1, jcomp=1, kcomp=1)
+            }
         elif dim == 3:
             self.kernel_dict = {
-                (3, 0, 0): StressletKernel(dim=3, icomp=0, jcomp=0, kcomp=0),
-                (2, 1, 0): StressletKernel(dim=3, icomp=0, jcomp=0, kcomp=1),
-                (2, 0, 1): StressletKernel(dim=3, icomp=0, jcomp=0, kcomp=2),
-                (1, 2, 0): StressletKernel(dim=3, icomp=0, jcomp=1, kcomp=1),
-                (1, 1, 1): StressletKernel(dim=3, icomp=0, jcomp=1, kcomp=2),
-                (1, 0, 2): StressletKernel(dim=3, icomp=0, jcomp=2, kcomp=2),
-                (0, 3, 0): StressletKernel(dim=3, icomp=1, jcomp=1, kcomp=1),
-                (0, 2, 1): StressletKernel(dim=3, icomp=1, jcomp=1, kcomp=2),
-                (0, 1, 2): StressletKernel(dim=3, icomp=1, jcomp=2, kcomp=2),
-                (0, 0, 3): StressletKernel(dim=3, icomp=2, jcomp=2, kcomp=2)
-                               }
-
+                (3, 0, 0): StressletComponentKernel(dim=3, icomp=0, jcomp=0, kcomp=0),
+                (2, 1, 0): StressletComponentKernel(dim=3, icomp=0, jcomp=0, kcomp=1),
+                (2, 0, 1): StressletComponentKernel(dim=3, icomp=0, jcomp=0, kcomp=2),
+                (1, 2, 0): StressletComponentKernel(dim=3, icomp=0, jcomp=1, kcomp=1),
+                (1, 1, 1): StressletComponentKernel(dim=3, icomp=0, jcomp=1, kcomp=2),
+                (1, 0, 2): StressletComponentKernel(dim=3, icomp=0, jcomp=2, kcomp=2),
+                (0, 3, 0): StressletComponentKernel(dim=3, icomp=1, jcomp=1, kcomp=1),
+                (0, 2, 1): StressletComponentKernel(dim=3, icomp=1, jcomp=1, kcomp=2),
+                (0, 1, 2): StressletComponentKernel(dim=3, icomp=1, jcomp=2, kcomp=2),
+                (0, 0, 3): StressletComponentKernel(dim=3, icomp=2, jcomp=2, kcomp=2)
+            }
         else:
-            raise ValueError("unsupported dimension given to StressletWrapper")
+            raise ValueError(f"unsupported dimension given to StressletWrapper: {dim}")
 
     def apply(self, density_vec_sym, dir_vec_sym, mu_sym, qbx_forced_limit):
         """Symbolic expressions for integrating Stresslet kernel.
diff --git a/test/extra_int_eq_data.py b/test/extra_int_eq_data.py
index 944ce5a70..b66edda9a 100644
--- a/test/extra_int_eq_data.py
+++ b/test/extra_int_eq_data.py
@@ -49,7 +49,7 @@
 
     from arraycontext import ArrayContext
     from boxtree.tree_build import ExtentNorm
-    from sumpy.kernel import Kernel
+    from sumpy.kernel import ScalarKernel
 
     from pytential.array_context import PyOpenCLArrayContext
     from pytential.symbolic.pde.scalar import L2WeightedPDEOperator
@@ -121,7 +121,7 @@ class IntegralEquationTestCase(ABC):
     ambient_dim: int = -1
 
     # operator
-    knl_class_or_helmholtz_k: type[Kernel] | int | float = 0
+    knl_class_or_helmholtz_k: type[ScalarKernel] | int | float = 0
     knl_kwargs: dict[str, Any] = field(default_factory=dict)
     bc_type: str = "dirichlet"
     side: int = -1
@@ -157,7 +157,7 @@ class IntegralEquationTestCase(ABC):
 
     @property
     @memoize_method
-    def knl_class(self) -> type[Kernel]:
+    def knl_class(self) -> type[ScalarKernel]:
         if isinstance(self.knl_class_or_helmholtz_k, type):
             return self.knl_class_or_helmholtz_k
 
diff --git a/test/test_layer_pot_identity.py b/test/test_layer_pot_identity.py
index eef7d8bb9..fe3eb8942 100644
--- a/test/test_layer_pot_identity.py
+++ b/test/test_layer_pot_identity.py
@@ -42,7 +42,7 @@
 )
 
 # from sumpy.visualization import FieldPlotter
-from sumpy.kernel import HelmholtzKernel, Kernel, LaplaceKernel
+from sumpy.kernel import HelmholtzKernel, LaplaceKernel, ScalarKernel
 
 from pytential import GeometryCollection, bind, norm, sym
 from pytential.array_context import PytestPyOpenCLArrayContextFactory
@@ -78,7 +78,7 @@ class IdentityExpr(ABC):
     order_drop: ClassVar[int]
 
     @abstractmethod
-    def get_zero_op(self, kernel: Kernel, **knl_kwargs: sym.Operand) -> sym.Operand:
+    def get_zero_op(self, kernel: ScalarKernel, **kwargs: sym.Operand) -> sym.Operand:
         pass
 
 
@@ -87,13 +87,13 @@ class GreenExpr(IdentityExpr):
     order_drop: ClassVar[int] = 0
 
     @override
-    def get_zero_op(self, kernel: Kernel, **knl_kwargs: sym.Operand) -> sym.Operand:
+    def get_zero_op(self, kernel: ScalarKernel, **kwargs: sym.Operand) -> sym.Operand:
         u_sym = sym.var("u")
         dn_u_sym = sym.var("dn_u")
 
         return (
-            sym.S(kernel, dn_u_sym, qbx_forced_limit=-1, **knl_kwargs)
-            - sym.D(kernel, u_sym, qbx_forced_limit="avg", **knl_kwargs)
+            sym.S(kernel, dn_u_sym, qbx_forced_limit=-1, **kwargs)
+            - sym.D(kernel, u_sym, qbx_forced_limit="avg", **kwargs)
             - 0.5*u_sym)
 
 
@@ -102,7 +102,7 @@ class GradGreenExpr(IdentityExpr):
     order_drop: ClassVar[int] = 1
 
     @override
-    def get_zero_op(self, kernel: Kernel, **knl_kwargs: sym.Operand) -> sym.Operand:
+    def get_zero_op(self, kernel: ScalarKernel, **kwargs: sym.Operand) -> sym.Operand:
         d = kernel.dim
         u_sym = sym.var("u")
         grad_u_sym = sym.make_sym_mv("grad_u", d)
@@ -110,9 +110,9 @@ def get_zero_op(self, kernel: Kernel, **knl_kwargs: sym.Operand) -> sym.Operand:
 
         return (
                 d1.resolve(d1.dnabla(d) * d1(sym.S(kernel, dn_u_sym,
-                    qbx_forced_limit="avg", **knl_kwargs)))
+                    qbx_forced_limit="avg", **kwargs)))
                 - d2.resolve(d2.dnabla(d) * d2(sym.D(kernel, u_sym,
-                    qbx_forced_limit="avg", **knl_kwargs)))
+                    qbx_forced_limit="avg", **kwargs)))
                 - 0.5*grad_u_sym
                 ).as_vector()
 
@@ -122,9 +122,9 @@ class ZeroCalderonExpr(IdentityExpr):
     order_drop: ClassVar[int] = 1
 
     @override
-    def get_zero_op(self, kernel: Kernel, **knl_kwargs: sym.Operand) -> sym.Operand:
+    def get_zero_op(self, kernel: ScalarKernel, **kwargs: sym.Operand) -> sym.Operand:
         assert isinstance(kernel, LaplaceKernel)
-        assert not knl_kwargs
+        assert not kwargs
 
         u_sym = sym.var("u")
 
diff --git a/test/test_symbolic.py b/test/test_symbolic.py
index 36049e815..f1ba0c040 100644
--- a/test/test_symbolic.py
+++ b/test/test_symbolic.py
@@ -466,9 +466,9 @@ def test_derivative_binder_expr():
 # {{{ test_mapper_kernel_transformation_remover
 
 def _make_operator(ambient_dim: int, op_name: str, k: float, *, side: int = +1):
-    from sumpy.kernel import HelmholtzKernel, Kernel, LaplaceKernel
+    from sumpy.kernel import HelmholtzKernel, LaplaceKernel, ScalarKernel
     if k == 0:
-        kernel: Kernel = LaplaceKernel(ambient_dim)
+        kernel: ScalarKernel = LaplaceKernel(ambient_dim)
         kernel_arguments = {}
     else:
         kernel = HelmholtzKernel(ambient_dim)