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+/*
+ * Relaxation solver for a 2nd order 2D linear PDE.
+ * Copyright 2018 Anton Khirnov <anton@khirnov.net>
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef MG2D_ELL_RELAX_H
+#define MG2D_ELL_RELAX_H
+
+/**
+ * The problem being solved is a linear partial differential
+ * equation
+ *
+ *   ∑ C_{ab} ∂_a　∂_b u  + ∑ C_{a} ∂_a u + C u = rhs
+ *  a,b                     a
+ *
+ *  where
+ *      * a and b identify spatial directions and run from 0 to 1
+ *      * u = u(x_a) is the unknown function
+ *      * C_{ab}, C_{a} and C are the coefficients in front of
+ *        the corresponding derivative of unknown function
+ *      * rhs is the right-hand side of the equation
+ * C_{*} and rhs are all (known) functions of space and define the
+ * equation to be solved.
+ */
+
+#include <stddef.h>
+#include <stdint.h>
+
+#include "log.h"
+
+/**
+ * Type of the boundary condition on a given boundary.
+ */
+enum EllRelaxBCType {
+    /**
+     * The value of the unknown function is fixed on the boundary.
+     */
+    ELL_RELAX_BC_TYPE_FIXVAL,
+    /**
+     * The normal derivative of the unkown function is fixed on the boundary.
+     *
+     * TODO: the only supported value of the derivative is currently zero, i.e.
+     * periodic boundary conditions.
+     */
+    ELL_RELAX_BC_TYPE_FIXDIFF,
+};
+
+/**
+ * Location of the boundary.
+ */
+enum EllRelaxBoundaryLoc {
+    /**
+     * Lower coord0, lower coord1.
+     */
+    ELL_RELAX_BOUNDARY_00,
+    /**
+     * Lower coord0, upper coord1.
+     */
+    ELL_RELAX_BOUNDARY_01,
+    /**
+     * Upper coord0, lower coord1.
+     */
+    ELL_RELAX_BOUNDARY_10,
+    /**
+     * Upper coord0, upper coord1.
+     */
+    ELL_RELAX_BOUNDARY_11,
+};
+
+/**
+ * Derivative specifier.
+ */
+enum EllRelaxDiffCoeff {
+    /**
+     * Zeroth derivative, i.e. function value.
+     */
+    ELL_RELAX_DIFF_COEFF_00,
+    /**
+     * First derivative wrt coord1.
+     */
+    ELL_RELAX_DIFF_COEFF_01,
+    /**
+     * First derivative wrt coord0.
+     */
+    ELL_RELAX_DIFF_COEFF_10,
+    /**
+     * Second derivative, once wrt coord0 and once wrt coord1
+     */
+    ELL_RELAX_DIFF_COEFF_11,
+    /**
+     * Second derivative wrt coord1
+     */
+    ELL_RELAX_DIFF_COEFF_02,
+    /**
+     * Second derivative wrt coord0
+     */
+    ELL_RELAX_DIFF_COEFF_20,
+    /**
+     * Total number of allowed derivatives.
+     */
+    ELL_RELAX_DIFF_COEFF_NB,
+};
+
+typedef struct EllRelaxInternal EllRelaxInternal;
+
+/**
+ * Boundary condition definition.
+ */
+typedef struct EllRelaxBoundary {
+    /**
+     * Type of the boundary condition.
+     */
+    enum EllRelaxBCType type;
+    /**
+     * For type = ELL_RELAX_BC_TYPE_FIXVAL:
+     *     Values of the unknown function on the boundary.
+     *
+     * Ignored otherwise.
+     */
+    double *val;
+    /**
+     * Number of elements in val.
+     */
+    size_t  val_len;
+} EllRelaxBoundary;
+
+typedef struct EllRelaxContext {
+    /**
+     * Solver private data, not to be accessed in any way by the caller.
+     */
+    EllRelaxInternal *priv;
+
+    /**
+     * The logging context, to be filled by the caller before mg2di_ell_relax_init().
+     */
+    MG2DLogger logger;
+
+    /**
+     * Size of the solver grid, set by mg2di_ell_relax_alloc().
+     * Read-only for the caller.
+     */
+    size_t domain_size[2];
+
+    /**
+     * Distance between the neighbouring grid points.
+     * Must be set by the caller before mg2di_ell_relax_init().
+     */
+    double step[2];
+
+    /**
+     * Order of the finite difference operators used for approximating derivatives.
+     * Must be set by the caller before mg2di_ell_relax_init().
+     */
+    size_t fd_stencil;
+
+    /**
+     * Boundary specification, indexed by EllRelaxBoundaryLoc.
+     * To be filled by the caller before mg2di_ell_relax_init().
+     */
+    EllRelaxBoundary boundaries[4];
+
+    /**
+     * Values of the unknown function.
+     *
+     * Allocated by the solver in mg2di_ell_relax_alloc(), owned by the solver.
+     * Must be filled by the caller before mg2di_ell_relax_init() to set the
+     * initial guess.
+     * Afterwards updated in mg2di_ell_relax_step().
+     */
+    double   *u;
+    /**
+     * Distance between neighbouring gridpoints along coord1.
+     */
+    ptrdiff_t u_stride;
+
+    /**
+     * Values of the right-hand side.
+     *
+     * Allocated by the solver in mg2di_ell_relax_alloc(), owned by the solver.
+     * Must be filled by the caller before mg2di_ell_relax_init().
+     */
+    double    *rhs;
+    /**
+     * Distance between neighbouring gridpoints along coord1.
+     */
+    ptrdiff_t  rhs_stride;
+
+    /**
+     * Values of the right-hand side.
+     *
+     * Allocated by the solver in mg2di_ell_relax_alloc(), owned by the solver.
+     * Read-only for the caller. Initialized after mg2di_ell_relax_init(),
+     * afterwards updated in mg2di_ell_relax_step().
+     */
+    double   *residual;
+    /**
+     * Distance between neighbouring gridpoints along coord1.
+     */
+    ptrdiff_t residual_stride;
+
+    /**
+     * Coefficients C_{*} that define the differential equation.
+     *
+     * Allocated by the solver in mg2di_ell_relax_alloc(), owned by the solver.
+     * Must be filled by the caller before mg2di_ell_relax_init().
+     */
+    double   *diff_coeffs[ELL_RELAX_DIFF_COEFF_NB];
+    /**
+     * Distance between neighbouring gridpoints along coord1.
+     */
+    ptrdiff_t diff_coeffs_stride;
+} EllRelaxContext;
+
+/**
+ * Allocate the solver for the given domain size.
+ *
+ * @param domain_size number of grid points in each direction.
+ *
+ * @return The solver context on success, NULL on failure.
+ */
+EllRelaxContext *mg2di_ell_relax_alloc(size_t domain_size[2]);
+/**
+ * Initialize the solver for use, after all the required fields are filled by
+ * the caller.
+ *
+ * This function may be called multiple times to re-initialize the solver after
+ * certain parameters (e.g. the right-hand side or the equation coefficients)
+ * change.
+ *
+ * @return 0 on success, a negative error code on failure.
+ */
+int              mg2di_ell_relax_init(EllRelaxContext *ctx);
+/**
+ * Free the solver and write NULL to the provided pointer.
+ */
+void             mg2di_ell_relax_free(EllRelaxContext **ctx);
+
+/**
+ * Perform a single relaxation step.
+ *
+ * @return 0 on success, a negative error code on failure.
+ */
+int mg2di_ell_relax_step(EllRelaxContext *ctx);
+
+#endif /* MG2D_ELL_RELAX_H */