specfem::point::displacement

template<specfem::dimension::type DimensionTag, specfem::element::medium_tag MediumTag, bool UseSIMD>
class displacement : public specfem::point::impl::field<DimensionTag, MediumTag, specfem::data_access::DataClassType::displacement, UseSIMD>

Point displacement field accessor for spectral element computations.

This class provides a specialized interface for accessing and manipulating displacement field data at individual points within spectral elements. It inherits all functionality from the base field implementation while being specifically typed for displacement data.

The displacement class is fundamental in wave propagation simulations, representing the spatial displacement of material points from their reference positions. It is commonly used in both elastic and poroelastic media simulations.

// Example: Creating 3D elastic displacement field accessor
using DispField = specfem::point::displacement<
    specfem::dimension::type::dim3,
    specfem::element::medium_tag::elastic,
    true>;   // Enable SIMD

// Initialize with zero displacement
DispField disp(0.0);

// Set displacement components
disp(0) = 0.001;  // x-component displacement (meters)
disp(1) = 0.002;  // y-component displacement
disp(2) = 0.003;  // z-component displacement

// Use in assembly operations
specfem::assembly::store_on_device(point_index, field_container, disp);


// Example: Computing strain from displacement gradients
DispField displacement;
specfem::assembly::load_on_device(index, fields, displacement);

// Access displacement components for strain computation
auto ux = displacement(0);
auto uy = displacement(1);
auto uz = displacement(2);

// Strain components would be computed from spatial derivatives
// (implementation depends on quadrature and differentiation operators)
’

See also

specfem::point::velocity for velocity field accessor

See also

specfem::point::acceleration for acceleration field accessor

See also

specfem::point::mass_inverse for inverse mass matrix field accessor

Template Parameters:

  • DimensionTag – The spatial dimension (dim2 or dim3) of the displacement field

  • MediumTag – The medium type (acoustic, elastic, poroelastic, etc.)

  • UseSIMD – Whether to enable SIMD vectorization for performance optimization

Public Types

using simd = typename base_type::simd

SIMD type for vectorized displacement operations.

using value_type = typename base_type::value_type

Vector type for storing displacement component values.

template<typename T>
using scalar_type = typename simd<T>::datatype

Scalar field storage for single point.

Template Parameters:

T – Base data type

template<typename T, int dimension>
using vector_type = typename specfem::datatype::VectorPointViewType<T, dimension, UseSIMD>

Vector field storage for single point.

Template Parameters:

  • T – Base data type

  • dimension – Vector dimension (2D/3D)

template<typename T, int components, int dimension>
using tensor_type = typename specfem::datatype::TensorPointViewType<T, components, dimension, UseSIMD>

Tensor field storage for single point.

Template Parameters:

  • T – Base data type

  • components – Number of tensor components

  • dimension – Spatial dimension

Public Functions

inline const value_type &get_data() const

Access internal field data storage.

Returns:

const reference to the internal value_type storing field components

inline const value_type::value_type &operator()(const std::size_t icomp) const

Access field component by index (const version).

Provides read-only access to individual field components using zero-based indexing. For 2D problems: 0=x, 1=z. For 3D problems: 0=x, 1=y, 2=z.

DisplacementField u_field(1.5, 2.3);
auto ux = u_field(0);  // x-component = 1.5
auto uz = u_field(1);  // z-component = 2.3

Parameters:

icomp – Component index (0 to components-1)

Returns:

const reference to the component value

Pre:

icomp must be less than the number of components

inline value_type::value_type &operator()(const std::size_t icomp)

Access field component by index (mutable version).

Provides read-write access to individual field components using zero-based indexing. Allows modification of field component values.

DisplacementField u_field;
u_field(0) = 1.5;  // Set x-component
u_field(1) = 2.3;  // Set z-component

Parameters:

icomp – Component index (0 to components-1)

Returns:

mutable reference to the component value

Pre:

icomp must be less than the number of components

inline bool operator==(const field &other) const

Equality comparison operator.

Compares two field objects for exact equality by comparing their internal data storage.

Parameters:

other – The field object to compare against

Returns:

true if all components are exactly equal, false otherwise

inline bool operator!=(const field &other) const

Inequality comparison operator.

Compares two field objects for inequality.

Parameters:

other – The field object to compare against

Returns:

true if any component differs, false if all components are equal

inline constexpr auto &operator*=(const typename value_type::value_type &other)

Multiplication assignment operator with constant value.

Multiply by a constant value and assign the result to this field.

Parameters:

other – The factor to be multiplied with

Returns:

reference to this field after multiplication

inline std::string print() const

Output a string representation of the field components.

Outputs the values of all field components to the specified output stream. Each component is printed in order, enclosed in square brackets. If SIMD the SIMD values are printed in curly brackets.

Public Static Attributes

static constexpr int components

Number of field components based on dimension and medium type.

static constexpr auto medium_tag

Medium tag identifying the physical medium type.

static constexpr auto accessor_type = specfem::data_access::AccessorType::point

Accessor pattern identifier.

static constexpr auto data_class = DataClass

Data classification type.

static constexpr auto dimension_tag = DimensionTag

Spatial dimension.

static constexpr bool using_simd = UseSIMD

SIMD vectorization flag.

specfem::point::velocity

template<specfem::dimension::type DimensionTag, specfem::element::medium_tag MediumTag, bool UseSIMD>
class velocity : public specfem::point::impl::field<DimensionTag, MediumTag, specfem::data_access::DataClassType::velocity, UseSIMD>

Point velocity field accessor for spectral element computations.

This class provides a specialized interface for accessing and manipulating velocity field data at individual points within spectral elements. It inherits all functionality from the base field implementation while being specifically typed for velocity data.

The velocity class represents the time derivative of displacement and is essential in time-domain wave propagation simulations. It is used in time integration schemes and for computing kinetic energy in the system.

// Example: Creating 2D acoustic velocity field accessor
using VelField = specfem::point::velocity<
    specfem::dimension::type::dim2,
    specfem::element::medium_tag::acoustic,
    false>;  // No SIMD

// Initialize with zero velocity
VelField vel(0.0);

// Set velocity components
vel(0) = 0.1;   // x-component velocity (m/s)
vel(1) = -0.05; // z-component velocity

// Use in assembly operations
specfem::assembly::load_on_device(point_index, field_container, vel);


// Example: Velocity in time integration (Newmark scheme)
VelField velocity_old, velocity_new;
AccelField acceleration;
const double dt = 0.001; // time step
const double gamma = 0.5; // Newmark parameter

// Load current values
specfem::assembly::load_on_device(index, fields, velocity_old, acceleration);

// Update velocity using Newmark scheme
for (int icomp = 0; icomp < VelField::components; ++icomp) {
  velocity_new(icomp) = velocity_old(icomp) + dt * gamma *
acceleration(icomp);
}

// Store updated velocity
specfem::assembly::store_on_device(index, fields, velocity_new);

See also

specfem::point::displacement for displacement field accessor

See also

specfem::point::acceleration for acceleration field accessor

See also

specfem::point::mass_inverse for inverse mass matrix field accessor

Template Parameters:

  • DimensionTag – The spatial dimension (dim2 or dim3) of the velocity field

  • MediumTag – The medium type (acoustic, elastic, poroelastic, etc.)

  • UseSIMD – Whether to enable SIMD vectorization for performance optimization

Public Types

using simd = typename base_type::simd

SIMD type for vectorized velocity operations.

using value_type = typename base_type::value_type

Vector type for storing velocity component values.

template<typename T>
using scalar_type = typename simd<T>::datatype

Scalar field storage for single point.

Template Parameters:

T – Base data type

template<typename T, int dimension>
using vector_type = typename specfem::datatype::VectorPointViewType<T, dimension, UseSIMD>

Vector field storage for single point.

Template Parameters:

  • T – Base data type

  • dimension – Vector dimension (2D/3D)

template<typename T, int components, int dimension>
using tensor_type = typename specfem::datatype::TensorPointViewType<T, components, dimension, UseSIMD>

Tensor field storage for single point.

Template Parameters:

  • T – Base data type

  • components – Number of tensor components

  • dimension – Spatial dimension

Public Functions

inline const value_type &get_data() const

Access internal field data storage.

Returns:

const reference to the internal value_type storing field components

inline const value_type::value_type &operator()(const std::size_t icomp) const

Access field component by index (const version).

Provides read-only access to individual field components using zero-based indexing. For 2D problems: 0=x, 1=z. For 3D problems: 0=x, 1=y, 2=z.

DisplacementField u_field(1.5, 2.3);
auto ux = u_field(0);  // x-component = 1.5
auto uz = u_field(1);  // z-component = 2.3

Parameters:

icomp – Component index (0 to components-1)

Returns:

const reference to the component value

Pre:

icomp must be less than the number of components

inline value_type::value_type &operator()(const std::size_t icomp)

Access field component by index (mutable version).

Provides read-write access to individual field components using zero-based indexing. Allows modification of field component values.

DisplacementField u_field;
u_field(0) = 1.5;  // Set x-component
u_field(1) = 2.3;  // Set z-component

Parameters:

icomp – Component index (0 to components-1)

Returns:

mutable reference to the component value

Pre:

icomp must be less than the number of components

inline bool operator==(const field &other) const

Equality comparison operator.

Compares two field objects for exact equality by comparing their internal data storage.

Parameters:

other – The field object to compare against

Returns:

true if all components are exactly equal, false otherwise

inline bool operator!=(const field &other) const

Inequality comparison operator.

Compares two field objects for inequality.

Parameters:

other – The field object to compare against

Returns:

true if any component differs, false if all components are equal

inline constexpr auto &operator*=(const typename value_type::value_type &other)

Multiplication assignment operator with constant value.

Multiply by a constant value and assign the result to this field.

Parameters:

other – The factor to be multiplied with

Returns:

reference to this field after multiplication

inline std::string print() const

Output a string representation of the field components.

Outputs the values of all field components to the specified output stream. Each component is printed in order, enclosed in square brackets. If SIMD the SIMD values are printed in curly brackets.

Public Static Attributes

static constexpr int components

Number of field components based on dimension and medium type.

static constexpr auto medium_tag

Medium tag identifying the physical medium type.

static constexpr auto accessor_type = specfem::data_access::AccessorType::point

Accessor pattern identifier.

static constexpr auto data_class = DataClass

Data classification type.

static constexpr auto dimension_tag = DimensionTag

Spatial dimension.

static constexpr bool using_simd = UseSIMD

SIMD vectorization flag.

specfem::point::acceleration

template<specfem::dimension::type DimensionTag, specfem::element::medium_tag MediumTag, bool UseSIMD>
class acceleration : public specfem::point::impl::field<DimensionTag, MediumTag, specfem::data_access::DataClassType::acceleration, UseSIMD>

Point acceleration field accessor for spectral element computations.

This class provides a specialized interface for accessing and manipulating acceleration field data at individual points within spectral elements. It inherits all functionality from the base field implementation while being specifically typed for acceleration data.

The acceleration class is commonly used in time-domain wave propagation simulations where acceleration values need to be computed, stored, and accessed at quadrature points during the assembly process.

// Example: Creating 2D elastic acceleration field accessor
using AccelField = specfem::point::acceleration<
    specfem::dimension::type::dim2,
    specfem::element::medium_tag::elastic,
    false>;  // No SIMD

// Initialize with zero acceleration
AccelField accel(0.0);

// Set acceleration components
accel(0) = 9.81;  // x-component acceleration
accel(1) = 0.0;   // z-component acceleration

// Use in assembly operations
specfem::assembly::load_on_device(point_index, field_container, accel);


// Example: Using acceleration in time integration scheme
AccelField acceleration;
VelocityField velocity;
DisplacementField displacement;

// Load current values
specfem::assembly::load_on_device(index, fields, acceleration, velocity,
displacement);

// Time integration (Newmark scheme)
for (int icomp = 0; icomp < AccelField::components; ++icomp) {
  velocity(icomp) += dt * acceleration(icomp);
  displacement(icomp) += dt * velocity(icomp) + 0.5 * dt * dt *
acceleration(icomp);
}

// Store updated values
specfem::assembly::store_on_device(index, fields, velocity, displacement);

See also

specfem::point::velocity for velocity field accessor

See also

specfem::point::displacement for displacement field accessor

See also

specfem::point::mass_inverse for inverse mass matrix field accessor

Template Parameters:

  • DimensionTag – The spatial dimension (dim2 or dim3) of the acceleration field

  • MediumTag – The medium type (acoustic, elastic, poroelastic, etc.)

  • UseSIMD – Whether to enable SIMD vectorization for performance optimization

Public Types

using simd = typename base_type::simd

SIMD type for vectorized acceleration operations.

using value_type = typename base_type::value_type

Vector type for storing acceleration component values.

template<typename T>
using scalar_type = typename simd<T>::datatype

Scalar field storage for single point.

Template Parameters:

T – Base data type

template<typename T, int dimension>
using vector_type = typename specfem::datatype::VectorPointViewType<T, dimension, UseSIMD>

Vector field storage for single point.

Template Parameters:

  • T – Base data type

  • dimension – Vector dimension (2D/3D)

template<typename T, int components, int dimension>
using tensor_type = typename specfem::datatype::TensorPointViewType<T, components, dimension, UseSIMD>

Tensor field storage for single point.

Template Parameters:

  • T – Base data type

  • components – Number of tensor components

  • dimension – Spatial dimension

Public Functions

inline const value_type &get_data() const

Access internal field data storage.

Returns:

const reference to the internal value_type storing field components

inline const value_type::value_type &operator()(const std::size_t icomp) const

Access field component by index (const version).

Provides read-only access to individual field components using zero-based indexing. For 2D problems: 0=x, 1=z. For 3D problems: 0=x, 1=y, 2=z.

DisplacementField u_field(1.5, 2.3);
auto ux = u_field(0);  // x-component = 1.5
auto uz = u_field(1);  // z-component = 2.3

Parameters:

icomp – Component index (0 to components-1)

Returns:

const reference to the component value

Pre:

icomp must be less than the number of components

inline value_type::value_type &operator()(const std::size_t icomp)

Access field component by index (mutable version).

Provides read-write access to individual field components using zero-based indexing. Allows modification of field component values.

DisplacementField u_field;
u_field(0) = 1.5;  // Set x-component
u_field(1) = 2.3;  // Set z-component

Parameters:

icomp – Component index (0 to components-1)

Returns:

mutable reference to the component value

Pre:

icomp must be less than the number of components

inline bool operator==(const field &other) const

Equality comparison operator.

Compares two field objects for exact equality by comparing their internal data storage.

Parameters:

other – The field object to compare against

Returns:

true if all components are exactly equal, false otherwise

inline bool operator!=(const field &other) const

Inequality comparison operator.

Compares two field objects for inequality.

Parameters:

other – The field object to compare against

Returns:

true if any component differs, false if all components are equal

inline constexpr auto &operator*=(const typename value_type::value_type &other)

Multiplication assignment operator with constant value.

Multiply by a constant value and assign the result to this field.

Parameters:

other – The factor to be multiplied with

Returns:

reference to this field after multiplication

inline std::string print() const

Output a string representation of the field components.

Outputs the values of all field components to the specified output stream. Each component is printed in order, enclosed in square brackets. If SIMD the SIMD values are printed in curly brackets.

Public Static Attributes

static constexpr int components

Number of field components based on dimension and medium type.

static constexpr auto medium_tag

Medium tag identifying the physical medium type.

static constexpr auto accessor_type = specfem::data_access::AccessorType::point

Accessor pattern identifier.

static constexpr auto data_class = DataClass

Data classification type.

static constexpr auto dimension_tag = DimensionTag

Spatial dimension.

static constexpr bool using_simd = UseSIMD

SIMD vectorization flag.

specfem::point::mass_inverse

template<specfem::dimension::type DimensionTag, specfem::element::medium_tag MediumTag, bool UseSIMD>
class mass_inverse : public specfem::point::impl::field<DimensionTag, MediumTag, specfem::data_access::DataClassType::mass_matrix, UseSIMD>

Point inverse mass matrix accessor for spectral element computations.

This class provides a specialized interface for accessing and manipulating inverse mass matrix data at individual points within spectral elements. It inherits all functionality from the base field implementation while being specifically typed for inverse mass matrix data.

The inverse mass matrix is crucial in explicit time integration schemes for wave propagation simulations. It allows for efficient computation of accelerations from forces without requiring matrix inversions during the time stepping process. The diagonal nature of the mass matrix in spectral element methods makes this particularly efficient.

// Example: Creating 2D elastic inverse mass matrix accessor
using MassInvField = specfem::point::mass_inverse<
    specfem::dimension::type::dim2,
    specfem::element::medium_tag::elastic,
    false>;  // No SIMD

// Initialize with uniform inverse mass
MassInvField mass_inv(1.0 / 2700.0);  // 1/density for elastic material

// Set component-specific inverse mass values
mass_inv(0) = 1.0 / mass_x;  // x-component inverse mass
mass_inv(1) = 1.0 / mass_z;  // z-component inverse mass

// Use in assembly operations
specfem::assembly::load_on_device(point_index, mass_container, mass_inv);


// Example: Using inverse mass matrix in explicit time integration
MassInvField mass_inverse;
AccelField acceleration;
ForceField internal_forces, external_forces;

// Load mass matrix and forces
specfem::assembly::load_on_device(index, fields, mass_inverse);
specfem::assembly::load_on_device(index, forces, internal_forces,
external_forces);

// Compute acceleration: a = M^(-1) * (F_ext - F_int)
for (int icomp = 0; icomp < MassInvField::components; ++icomp) {
  acceleration(icomp) = mass_inverse(icomp) *
                       (external_forces(icomp) - internal_forces(icomp));
}

// Store computed acceleration
specfem::assembly::store_on_device(index, fields, acceleration);

See also

specfem::point::displacement for displacement field accessor

See also

specfem::point::velocity for velocity field accessor

See also

specfem::point::acceleration for acceleration field accessor

Template Parameters:

  • DimensionTag – The spatial dimension (dim2 or dim3) of the mass matrix field

  • MediumTag – The medium type (acoustic, elastic, poroelastic, etc.)

  • UseSIMD – Whether to enable SIMD vectorization for performance optimization

Public Types

using simd = typename base_type::simd

SIMD type for vectorized inverse mass matrix operations.

using value_type = typename base_type::value_type

Vector type for storing inverse mass matrix component values.

template<typename T>
using scalar_type = typename simd<T>::datatype

Scalar field storage for single point.

Template Parameters:

T – Base data type

template<typename T, int dimension>
using vector_type = typename specfem::datatype::VectorPointViewType<T, dimension, UseSIMD>

Vector field storage for single point.

Template Parameters:

  • T – Base data type

  • dimension – Vector dimension (2D/3D)

template<typename T, int components, int dimension>
using tensor_type = typename specfem::datatype::TensorPointViewType<T, components, dimension, UseSIMD>

Tensor field storage for single point.

Template Parameters:

  • T – Base data type

  • components – Number of tensor components

  • dimension – Spatial dimension

Public Functions

inline const value_type &get_data() const

Access internal field data storage.

Returns:

const reference to the internal value_type storing field components

inline const value_type::value_type &operator()(const std::size_t icomp) const

Access field component by index (const version).

Provides read-only access to individual field components using zero-based indexing. For 2D problems: 0=x, 1=z. For 3D problems: 0=x, 1=y, 2=z.

DisplacementField u_field(1.5, 2.3);
auto ux = u_field(0);  // x-component = 1.5
auto uz = u_field(1);  // z-component = 2.3

Parameters:

icomp – Component index (0 to components-1)

Returns:

const reference to the component value

Pre:

icomp must be less than the number of components

inline value_type::value_type &operator()(const std::size_t icomp)

Access field component by index (mutable version).

Provides read-write access to individual field components using zero-based indexing. Allows modification of field component values.

DisplacementField u_field;
u_field(0) = 1.5;  // Set x-component
u_field(1) = 2.3;  // Set z-component

Parameters:

icomp – Component index (0 to components-1)

Returns:

mutable reference to the component value

Pre:

icomp must be less than the number of components

inline bool operator==(const field &other) const

Equality comparison operator.

Compares two field objects for exact equality by comparing their internal data storage.

Parameters:

other – The field object to compare against

Returns:

true if all components are exactly equal, false otherwise

inline bool operator!=(const field &other) const

Inequality comparison operator.

Compares two field objects for inequality.

Parameters:

other – The field object to compare against

Returns:

true if any component differs, false if all components are equal

inline constexpr auto &operator*=(const typename value_type::value_type &other)

Multiplication assignment operator with constant value.

Multiply by a constant value and assign the result to this field.

Parameters:

other – The factor to be multiplied with

Returns:

reference to this field after multiplication

inline std::string print() const

Output a string representation of the field components.

Outputs the values of all field components to the specified output stream. Each component is printed in order, enclosed in square brackets. If SIMD the SIMD values are printed in curly brackets.

Public Static Attributes

static constexpr int components

Number of field components based on dimension and medium type.

static constexpr auto medium_tag

Medium tag identifying the physical medium type.

static constexpr auto accessor_type = specfem::data_access::AccessorType::point

Accessor pattern identifier.

static constexpr auto data_class = DataClass

Data classification type.

static constexpr auto dimension_tag = DimensionTag

Spatial dimension.

static constexpr bool using_simd = UseSIMD

SIMD vectorization flag.

Implementation Details